Algebra and Trigonometry (4th Edition)
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domain, range ; The domain is the set of all ... more
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In mathematics, a function from a set X to another... more
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; Let be the input value.Multiply by , ... more
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; Let be the input value.Square .Add to the ... more
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; Let be the input value.Subtract from , .... more
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; Let be the input value.Add to , .Take the ... more
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Multiply by , then add . ; Use the order of ... more
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Add , then divide by . ; Use the order of ... more
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Add , then multiply by . ; Use the order of ... more
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Square, subtract , then divide by . ; Use the ... more
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, , , ; Replace input value with and simplify... more
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, , , , ; Replace input value with and ... more
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, , , , ; Replace input value with and ... more
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, , , , ; Replace input value with ... more
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, , , ; Replace input value with and ... more
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, is undefined, , , ; Replace input value ... more
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, , , , ; Replace input value with and ... more
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, , , , ; Replace input value with ... more
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, , , , ; Replace input value with ... more
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, , is undefined , , ; Replace input ... more
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, , , ; Since , use .Replace input value ... more
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, , , ; Since , use .Replace input value ... more
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, , , ; Since , use .Replace input value ... more
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, , , ; Since , use .Replace input value ... more
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, ; Replace input value, , with . ; Multiply ... more
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, ; Replace input value with and simplify... more
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, ; Replace input value with and simplify... more
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; Replace input value with and simplify. ; ... more
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; Determine by replacing the input value with ... more
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; Determine by replacing the input value with ... more
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; Determine by replacing the input value with ... more
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; Determine by replacing the input value with ... more
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, , ; Replace input value, , with . ; Replace ... more
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; Replace input value, , with . ; Replace input ... more
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; Replace input value, , with . ; Replace input ... more
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, , ; Replace input value, , with . ; ; ... more
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, , ; Replace input value, , with . ; Replace ... more
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, , ; Replace input value, , with . ; Replace ... more
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, , ; Replace input value, , with . ; Replace ... more
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, , ; Replace input value, , with . ; Replace ... more
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Domain: , Range: ; Excluded values in the domain ... more
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Domain: , Range: ; Excluded values in the domain ... more
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Domain: , Range: ; The possible values for the ... more
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Domain: , Range: ; The possible values for the ... more
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Domain: ; Determine what value of will make the ... more
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Domain: ; Determine what value of will make the ... more
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Domain: ; Determine what values of will make the ... more
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Domain: ; Determine what values of will make the ... more
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Domain: ; Determine when is greater than or equal... more
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Domain: ; Determine when is greater than or equal... more
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Domain: ; The radicand for cube roots can be any ... more
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Domain: ; Determine when is greater than or equal... more
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Domain: ; Determine when is greater than or equal... more
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Domain: ; Determine when is greater than or equal... more
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Domain: ; Determine what value of makes . ; Write... more
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Domain: ; Determine the interval over which gives... more
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Domain: ; Determine when .First factor . ; Use the... more
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Domain: ; Determine when .First factor . ; Use the... more
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Domain: ; The radicand can not be zero or negative... more
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Domain: ; The radicand can not be zero or negative... more
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Domain: ; The radicand can not be zero or negative... more
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Domain: ; The radicand can not be zero or negative... more
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Domain: , Range: ; Determine the domain. ; The ... more
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Domain: , Range: {1, all real irrational numbers... more
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The first line segment is shorter than the other ... more
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This is a rough graph. The graph starts with ... more
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This a rough graph of the given table. ; The ... more
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This a rough graph of the given table. ; The ... more
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Wages, gasoline for vehicle, sales tax on ... more
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Verbal: The employee’s wages are determined by ... more
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for for ; The... more
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, , , . ; When graphing a function, first replace... more
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; When graphing an ordered pair of a function, ... more
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; An ordered pair on the graph of a function is ... more
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is an even power function. Thus, it is a U-shaped... more
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Fill in the table by substituting each -value into... more
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Fill in the table by substituting each -value into... more
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Fill in the table by substituting each -value into... more
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Fill in the table by substituting each -value into... more
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Generate points for the graph. Write the points as... more
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Generate points for the graph. Write the points as... more
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Generate points for the graph. Write the points as... more
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Generate points for the graph. Write the points as... more
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Generate points for the graph. Write the points as... more
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Generate points for the graph. Write the points as... more
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Generate points for the graph. Write the points as... more
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Generate points for the graph. Write the points as... more
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Create a table of values with 3 columns. First ... more
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Create a table of values with 3 columns. First ... more
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Create a table of values with 3 columns. First ... more
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Create a table of values with 3 columns. First ... more
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Create a table of values with 3 columns. First ... more
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Create a table of values with 3 columns. First ... more
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Create a table of values with 3 columns. First ... more
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Create a table of values with 3 columns. First ... more
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Create a table of values with 3 columns. First ... more
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Create a table of values with 3 columns. First ... more
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Create a table of values with 3 columns. First ... more
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Create a table of values with 3 columns. First ... more
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The piecewise defined function is composed of two ... more
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The piecewise defined function is composed of two ... more
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The piecewise defined function is composed of two ... more
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The piecewise defined function is composed of two ... more
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The piecewise defined function is composed of two ... more
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The piecewise defined function is composed of two ... more
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The piecewise defined function is composed of ... more
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The piecewise defined function is composed of ... more
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The piecewise defined function is composed of two ... more
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The piecewise defined function is composed of two ... more
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Find the equivalent inequalities of the given ... more
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Find the equivalent inequalities of the given ... more
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The piecewise defined function is composed of ... more
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The piecewise defined function is composed of ... more
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Use a graphing utility to graph the given ... more
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Use a graphing utility to graph the given ... more
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; The graph in the interval is a horizontal line... more
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; The graph in the interval is a horizontal line... more
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YesDomain: Range: ; According to the Vertical ... more
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According to the Vertical Line Test, if no ... more
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According to the Vertical Line Test, if no ... more
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YesDomain: Range: ; According to the Vertical Line... more
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Solve for :Subtract from both sides.Divide both ... more
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Solve for :Subtract from both sides.Multiply both... more
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Take the square root of both sides to solve for... more
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Solve for :Subtract from both sides.Take the ... more
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Solve for :Subtract from both sides.Divide both ... more
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Solve for :Subtract from both sides.Divide both ... more
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Write the equation in the form :Subtract from ... more
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Solve for :Add to both sides.Square both sides.... more
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Subtract from both sides to solve for . A ... more
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Solve for :Subtract from both sides.Note that the... more
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Take the cube root of both sides to solve for . A... more
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Solve for :Take the square root of both sides.Drop... more
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; Find the slope of the line segment with end ... more
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; Find the slope of the line segment with end ... more
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; Solve for :Subtract from both sides.Take the ... more
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; Solve for :Subtract from both sides.Take the ... more
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Graph the function using a graphing utility:Use ... more
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Graph the function using a graphing utility:Use ... more
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; Since, the cost of the first mile is , for . ... more
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; Find the function: The fixed cost for the first... more
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A vertical line intersects the graph of the ... more
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Example 1: The cost of tutoring service for ... more
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Shrinking the graph of horizontally by a factor ... more
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a ; The function value is the number of ticks ... more
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; By definition, the domain is the set of all ... more
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; The -axis lies where the function value, ... more
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The race was between three runners A, B, and C.... more
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; Graph using a graphing utility. ; Adjust the ... more
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; Graph using a graphing utility. ; Adjust the ... more
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; Graph using a graphing utility.The graph below... more
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Listed below are some simple real-world situations... more
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; The average speed is defined by the distance ... more
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; The average rate of change measures the slope ... more
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; Evaluate at . ; Evaluate at . ; Solve for the... more
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; Both functions started with the same value at .... more
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At , the rate of increase in the value of was the... more
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; Take the difference in the water level for the ... more
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YearNumber ... more
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degrees/min; degrees/min;The temperature dropped ... more
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Ave. SpeedAs the intervals get smaller, the speed ... more
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15 ; Identify two ordered pairs that lie on the ... more
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15 gal/min ; From the graph, the slope of the line... more
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Up ; A positive rate of change means that as the -... more
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YesSlope: 0Rate of change: 0 ; The given function ... more
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Yes; . ; Under the commutative property of ... more
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Yes; . ; Under the commutative property of ... more
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Not linear ; First, expand the function by ... more
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Not linear ; The variable in the function is ... more
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Yes; . ; The function can be separated into two ... more
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Not linear ; The function can be separated into ... more
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Not linear ; Simplify the given by expanding the ... more
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Yes ; Simplify the given by distributing over the ... more
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; Create a table of values for using any value ... more
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; Create a table of values for using any value ... more
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; Create a table of values for using any value ... more
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; Create a table of values for using any value ... more
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; Write the linear function where is the rate of ... more
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; Write the linear function where is the rate of ... more
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; Write the linear function as Use since the ... more
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; Write the linear function as Use since the ... more
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As increases, the line defined by becomes steeper.... more
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As increases, the graph of the line defined by ... more
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for person B; for person M ; Determine the slope... more
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; Calculate for the run.The formula of the slope ... more
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symmetry about the -axis ; In an even function, ... more
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symmetry about the origin ; In an odd function, ... more
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Let be equal to , so that . Write the function ... more
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Let be equal to , so that . Write the function ... more
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Let be equal to , so that . Write the function ... more
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Let be equal to , so that . Write the function ... more
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Let be equal to , so that . Write the function ... more
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Let be equal to , so that . Write the function ... more
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Let be equal to , so that . Write the function ... more
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Let be equal to , so that . Write the function ... more
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Let be equal to , so that . Write the function ... more
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Let be equal to , so that . Write the function ... more
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Let be equal to the given function. Then, let be... more
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Let be equal to the given function. Then, let be... more
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Let be equal to the given function. Then, let be... more
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Let be equal to the given function. Then, let be... more
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Let be equal to the given function. Then, let be... more
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Let be equal to the given function. Then, let be... more
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Let be equal to the given function. Then, let be... more
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Let be equal to the given function. Then, let be... more
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Let be equal to the given function. Rewrite so ... more
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Let be equal to the given function. Rewrite so ... more
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Let be equal to the given function. Then, let be... more
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Let be equal to the given function. Rewrite f(x) ... more
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Let be equal to the given function. Then, let be... more
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Let be equal to the given function. Rewrite so ... more
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; Let the final function be equal to . Since the ... more
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; Let the final function be equal to . Since the ... more
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; Let the final function be equal to . Since the ... more
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; Let the final function be equal to . Since the ... more
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; Since the graph moves to the left, add to , ... more
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; Since the graph is reflected across the -axis, ... more
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; Since the graph is reflected across the ... more
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; Since the graph moves to the left, add to , ... more
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; Multiply by to denote the vertical stretching... more
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; Multiply by to denote the vertical shrinking.... more
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; Use the vertices of the functions as reference ... more
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; Use the inflection points of the functions as ... more
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; Use the vertices of the absolute value ... more
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; Write in terms of . The graph of is ... more
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; Use the starting points of the functions as ... more
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; Use the vertices of the functions as reference ... more
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The figure shows the graph of shifted 3 units up... more
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The figure shows the graph of shifted 4 units to ... more
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Determine the horizontal span of each step in the ... more
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Determine the horizontal span of each step in the ... more
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Even ; Check if the function is even or odd. ... more
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Odd ; Check if the function is even or odd. ... more
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Neither ; Check if the function is even or odd. ... more
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Even ; Check if the function is even or odd. ... more
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Odd ; Check if the function is even or odd. ... more
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Neither ; Check if the function is even or odd. ... more
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Neither ; Check if the function is even or odd. ... more
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Odd ; Check if the function is even or odd. ... more
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The graph of is the graph of , reflected across ... more
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Identify the part of the graph of for which the ... more
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Yes; shift the function 4 units to the right and ... more
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yes; reflect the graph of across the -axis, ... more
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Case 1: The functions and are both even.Let be ... more
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Case 1: The functions and are both even.Let be ... more
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To make an even function, should be an even ... more
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8 ; Add the values of and .Read the value of on ... more
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; The small circle in between and symbolizes ... more
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multiplication by 2 comes first, then adding 1 to ... more
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; The operation for can be written as . ; The ... more
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; The composite function can be written as , ... more
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Domain of : Domain of : Domain of : Domain of... more
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Domain of : Domain of : Domain of : Domain of... more
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Domain of : Domain of : Domain of : Domain of... more
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Domain of : Domain of : Domain of : Domain of... more
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Domain of : Domain of : Domain of : Domain of... more
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Domain of : Domain of : Domain of : Domain of... more
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Domain of : Domain of : Domain of : Domain of... more
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Domain of : Domain of : Domain of : Domain of... more
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Domain of : Domain of : Domain of : Domain of... more
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Domain of : Domain of : Domain of : Domain of... more
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; Separate the function into two parts.Let and... more
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; Separate the function into two parts.Let and... more
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; Express the given function as , then find the ... more
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; Separate the function into two parts.Let and... more
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To graphically add and , add a segment with the ... more
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To graphically add and , add a segment with the ... more
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Set the window settings of the graphing utility to... more
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Set the window settings of the graphing utility to... more
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Set the window settings of the graphing utility to... more
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Set the window settings of the graphing utility to... more
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4 ; Using the graph of , read the value at . ; ... more
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3 ; The given expression refers to the value of ... more
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5 ; The given expression refers to the value of ... more
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; The given expression refers to the value of ... more
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; The given expression means which refers to the... more
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; The given expression means which refers to the... more
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; The given expression refers to the value of ... more
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; The given expression refers to the value of ... more
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; The given expression refers to the value of ... more
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; The given expression refers to the value of ... more
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; Write the given expression as which refers to ... more
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; Write the given expression as which refers to ... more
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; Write the given expression as which refers to ... more
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; Write the given expression as which refers to ... more
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, , , , ; Find .Substitute for the ... more
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, , , , ; Find .Substitute for the variable... more
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, , , , ; Find .Substitute for the variable... more
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, , , , ; Find .Substitute for the variable... more
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, , , , ; Find . Substitute for the ... more
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, , , , ; Find . Substitute for the variable... more
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, , , , ; Find . Substitute for the variable... more
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, , , , ; Find . Substitute for the variable... more
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, , , , ; Find . Substitute for every ... more
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, , , , ; Find . Substitute for the variable... more
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; Find . Substitute for every variable in .... more
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; Find . Substitute for the variable in .... more
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; Find . Substitute for in . ; Find . ... more
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; Find . Substitute for in . ; Find . ... more
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; Find . Substitute for in . ; Find . ... more
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; Find . Substitute for in . ; Find . ... more
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; ; involves two operations: subtracting 9 ... more
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; ; involves two operations: taking the square... more
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; ; says to first square a number, and then ... more
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, ; Observe the function :First, 3 is added to... more
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; ; says to first subtract the cube of a number ... more
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; ; says to add one to the square root of a ... more
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; ; ; says to first square a number, add one ... more
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; ; ; says to first take the square root of a... more
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; ; ; says to first take the cube root of a ... more
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; ; ; says to first add 3 to the square root ... more
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Yes, ; Find . Substitute for in . Simplify. ; ... more
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; Find . Consider as an input to a function and... more
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; Substitute for in . ; more
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; Find the revenue function by multiplying the ... more
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; The surface area of a spherical solid is given ... more
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represents the amount of investment after two ... more
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If is even, is even.If is odd and is odd, is ... more
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different ; If a function is one-to-one then for ... more
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Yes, , ; Apply the horizontal line test to the ... more
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4, 3 ; The graph of the function and the graph of... more
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No ; Apply horizontal line test to the given graph... more
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Yes ; Apply horizontal line test to the given ... more
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Yes ; Apply horizontal line test to the given ... more
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No ; Apply horizontal line test to the given graph... more
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No ; Apply horizontal line test to the given graph... more
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Yes ; Apply horizontal line test to the given ... more
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Yes ; If the function is one-to-one, then for , ... more
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Yes ; If the function is one-to-one, then for , ... more
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Yes ; The square root of a positive number is a ... more
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No ; If the function is one-to-one, then for , ... more
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No ; If the function is one-to-one, then for , ... more
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Yes ; If the function is one-to-one, then for , ... more
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No ; If the function is one-to-one, then for , ... more
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Yes ; If the function is one-to-one, then for , ... more
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Yes ; If the function is one-to-one, then for , ... more
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No ; If the function is one-to-one, then for , ... more
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No ; If the function is one-to-one, then for , ... more
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Yes ; If the function is one-to-one, then for , ... more
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1 ; Since function is one-to-one, the inverse ... more
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1 ; Since function is one-to-one, the inverse ... more
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4 ; Since function is one-to-one, the inverse ... more
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; Determine from the table by identifying the ... more
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; Determine from the table. ; Replace by in ... more
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; Determine from the table by identifying the ... more
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; Determine from the table by identifying the ... more
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; Determine from the table by identifying the ... more
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Since and , and are inverses of each other. ; ... more
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Since and , and are inverses of each other. ; ... more
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Since and , and are inverses of each other. ; ... more
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Since and , and are inverses of each other. ; ... more
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Since and , and are inverses of each other. ; ... more
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Since and , and are inverses of each other. ; ... more
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Since and , and are inverses of each other. ; ... more
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Since and , and are inverses of each other. ; ... more
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Since and , and are inverses of each other. ; ... more
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Since and , and are inverses of each other. ; ... more
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Since and , and are inverses of each other... more
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Since and , and are inverses of each other. ; ... more
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; Write .Solve for in terms of . ; Interchange ... more
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; Write .Solve for in terms of . ; Interchange ... more
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; Write .Solve for in terms of . ; Interchange ... more
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; Write .Solve for in terms of . ; Interchange ... more
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; Write .Solve for in terms of . ; Interchange ... more
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; Write , then solve for in terms of .Cross ... more
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; Write , then solve for in terms of .Cross ... more
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; Write , then solve for in terms of .Cross ... more
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; Write , then solve for in terms of .Cross ... more
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; Write , then solve for in terms of .Cross ... more
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; Write , then solve for in terms of .Cross ... more
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; Write , then solve for in terms of .Cross ... more
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; Write .Solve for in terms of .The domain is ... more
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; Write .Complete the square and solve for in ... more
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; Write .Solve for in terms of .The domain is ... more
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; Write .Solve for in terms of .The domain is ... more
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; Write .Solve for in terms of . ; Interchange ... more
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; Write .Solve for in terms of . ; Interchange ... more
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; Write .Solve for in terms of . ; Interchange ... more
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; Write .Solve for in terms of . ; Interchange ... more
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; Write .Solve for in terms of . ; Interchange ... more
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; Write .Solve for in terms of .The domain is ... more
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Not one-to-one ; Enter the given function as into... more
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One-to-one ; Enter the given function as into one... more
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One-to-one ; Enter the given function as into one... more
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Not one-to-one ; Enter the given function as into... more
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Not one-to-one ; Enter the given function as ... more
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One-to-one ; Enter the given function as into ... more
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Domain restriction on : ; Restrict the domain of... more
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Domain restriction on : ; Restrict the domain of... more
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Domain restriction on : ; Restrict the domain of... more
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Domain restriction on : ; Restrict the domain ... more
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Create a table of function values from the given ... more
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Create a table of function values from the graph ... more
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Yesslope: ; The function represents a line for a ... more
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Prove :Prove :Prove :Prove : ; Assume that .Prove... more
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Verbal: by using words to describe the ... more
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Definition: A piecewise defined function is ... more
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Take the -coordinate of the given point to find . ... more
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is the maximum value of near . ; If is a local ... more
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Evaluate for and . Subtract the resulting ... more
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; Express the function in terms of .Square .Then... more
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; Express the function in terms of .Divide by 2.... more
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Add 10, then multiply the sum by 3. ; Describe the... more
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Multiply by 6, subtract 10, then take the square ... more
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; Substitute the different values for into the ... more
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; Substitute the different values for into the ... more
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; Substitute 0 for into , then evaluate the ... more
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; Substitute 5 for into , then evaluate the ... more
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domain: range: ; Find the domain. The radicand, , ... more
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domain: range: ; The given function does not ... more
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; The given function is linear and is defined for... more
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; Determine the -values that would make the ... more
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; The radicand, , must be greater than or equal ... more
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; Separate the function into two parts.Let and .... more
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; Separate the function into three parts.Let , , ... more
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; Find the -values that would make the ... more
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; Separate the function into two parts.Let and .... more
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; Separate the function into two parts.Let and .... more
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The exponents of the function are whole numbers ... more
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When the exponents of a function are whole numbers... more
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Let .Multiply by 3.Therefore, . ; Graph . ; Since... more
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Let . Multiply by .Therefore, . ; Graph . ; Since... more
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Let .Multiply by 2.Then, subtract 1 from .... more
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Let .Substitute for into .Then, multiply by .... more
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Rearrange the function so that the term is first... more
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Rearrange the function so that the -term is first... more
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Let .Multiply by .Therefore, . ; Graph . ; Since ... more
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Let .Substitute for into .Therefore, . ; Graph... more
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Let .Multiply by .Therefore, . ; Graph . ; Since... more
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Let .Substitute for into .Therefore, . ; Graph... more
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Determine what transformations are occurring.Let... more
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Determine what transformations are occurring.Let... more
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Make a table of different -values within the ... more
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Make a table of different -values within the ... more
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Isolate on the left side of the equation. ; Take ... more
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Isolate on the left side of the equation. ; ... more
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Isolate on the left side of the equation. ; Take ... more
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Isolate on the left side of the equation. ; Take ... more
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Adjust the window settings to and . Input the ... more
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Adjust the window settings to and .Input the ... more
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increasing , decreasing ; Adjust the window ... more
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increasing , decreasing , ; Adjust the window ... more
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Net change: Average rate of change: ; Let and . ... more
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Net change: Average rate of change: ; Let and . ... more
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Net change: Average rate of change: ; Let and . ... more
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Net change: Average rate of change: ; Let and . ... more
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Net change: Average rate of change: ; Substitute ... more
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Net change: Average rate of change: ; Substitute ... more
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Expand the square on the right side of the ... more
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Separate the fraction into two terms. ; The ... more
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; A linear function is in the form of , where is... more
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; A linear function is in the form of , where is... more
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; Select any two points, , from the table to find... more
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; Select any two points, , from the table to find... more
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; Find two points on the graph. The easiest ... more
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; Find two points on the graph. The easiest ... more
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local minimum at ; Adjust the window settings of ... more
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local maximum at . ; Adjust the window settings ... more
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local minimum: at local maximum: at ; Adjust the... more
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local minimum: at local maximum: at . ; Adjust ... more
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68 feet ; Adjust the window settings of the ... more
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units ; Adjust the window settings of the ... more
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Adjust the window settings of the graphing utility... more
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Adjust the window settings of the graphing utility... more
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, domain: , domain: , domain: , domain: ; can ... more
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, , , , ; Find . Substitute for in .Rationalize... more
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; The composition means . Find first by ... more
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, , ; says to take the square root of a number, ... more
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one-to-one ; A function is one-to-one if no two ... more
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not one-to-one ; A function is one-to-one if no ... more
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not one-to-one ; A function is one-to-one if no ... more
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one-to-one ; A function is one-to-one if no two ... more
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not one-to-one ; A function is one-to-one if no ... more
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one-to-one ; A function is one-to-one if no two ... more
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; Substitute for and then interchange variables... more
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; Substitute for and then interchange and . ; ... more
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; Substitute for and then interchange and . ; ... more
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; Substitute for and then interchange and . ; ... more
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yes, 1, 3 ; A function has an inverse if it is one... more
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no ; A function has an inverse if it is one-to-one... more
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Net Change: Ave R of C: ; Net change refers to ... more
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Since , and are inverse functions. ; Two ... more
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for ; Replace with .Interchange and variables ... more
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Domain: Range: ; Domain is a set of all ... more
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1 ; 3 ; means the -value of the graph when .Locate... more
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The graph of is similar to the graph of but ... more
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5 ; , respectively ; Net change is equal to the ... more
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0 ; 4 ; means the value of when .Locate on the ... more
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Locate some arbitrary points on the graph of . ; ... more
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for . ; The area of a rectangle is given by . ... more
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for . ; The area of a rectangular figure is given ... more
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for . ; The volume of a rectangular solid is given... more
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for . ; A cylinder is a solid figure with 2 ... more
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for . ; Perimeter is the distance around a figure... more
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for . ; The area of a rectangular shape is given ... more
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for . ; An equilateral triangle is a triangle with... more
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for . ; A cube is a 3-dimensional solid whose ... more
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for . ; The area of a circle is given by .Solve ... more
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for . ; The circumference of a circle is given by... more
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for . ; The volume of a rectangular solid with ... more
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for . ; Show that the two overlapping triangles ... more
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for . ; Let be the distance travelled by the boat... more
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for . ; Let be the second nonnegative number. ... more
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for . ; An isosceles triangle is a triangle with 2... more
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for . ; The perimeter of a triangle refers to the ... more
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for . ; Label the center of the circle and the ... more
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for . ; The volume of a cone is one-third the ... more
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50 and 50 ; Represent the two numbers. Let be the... more
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width length ; Let be the area of the rectangle. ... more
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