Test Bank for Precalculus Concepts Through Functions A Unit Circle Approach to Trigonometry 3r Full file Functions and Their Graphs at https://TestbankDirect.eu/ Ch. 1 1.1 Functions Determine Whether a Relation Represents a Function MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Determine whether the relation represents a function. If it is a function, state the domain and range 1) 4 → 20 → 30 → 40 10 → 50 A) function domain: {4, 6, 8, 10} range: {20, 30, 40, 50} B) function domain:{20, 30, 40, 50} range: {4, 6, 8, 10} C) not a function B) function domain: {snake, cat, dog} range: {Alice, Brad, Carl} C) not a function B) function domain: {cat, dog} range: {Alice, Brad, Carl} C) not a function 4) {(-3, -8), (2, 3), (3, 2), (6, -2)} A) function domain: {-3, 2, 3, 6} range: {-8, 3, 2, -2} B) function domain: {-8, 3, 2, -2} range: {-3, 2, 3, 6} C) not a function 5) {(5, -4), (1, -3), (1, 0), (10, 3), (26, 5)} A) function domain: {5, 10, 1, 26} range: {-4, -3, 0, 3, 5} B) function domain: {-4, -3, 0, 3, 5} range: {5, 10, 1, 26} C) not a function 6) {(-3, 10), (-2, 5), (0, 1), (2, 5), (4, 17)} A) function domain: {-3, -2, 0, 2, 4} range: {10, 5, 1, 17} B) function domain: {10, 5, 1, 17} range: {-3, -2, 0, 2, 4} C) not a function 2) Alice Brad Carl snake cat dog A) function domain: {Alice, Brad, Carl} range: {snake, cat, dog} 3) Alice Brad Carl cat dog A) function domain: {Alice, Brad, Carl} range: {cat, dog} Page 1 Copyright © 2015 Pearson Education, Inc Full file at https://TestbankDirect.eu/ Test Bank for Precalculus Concepts Through Functions A Unit Circle Approach to Trigonometry 3r Full file at https://TestbankDirect.eu/ 7) {(6.99, 8.69), (6.999, -8.7), ( , 0), (2.33, -6)} A) function domain: {6.99, 6.999, , 2.33} range: {8.69, -8.7, 0, -6} B) function domain: {8.69, -8.7, 0, -6} range: {6.99, 6.999, , 2.33} C) not a function Determine whether the equation defines y as a function of x 8) y = x3 A) function 9) y = B) not a function x A) function B) not a function 10) y = |x| A) function B) not a function 11) y2 = 2 - x2 A) function B) not a function 12) y = ± 1 - 3x A) function B) not a function 13) x = y2 A) function B) not a function 14) y2 + x = 5 A) function B) not a function 15) y = 3x2 - 4x + A) function B) not a function 16) y = 3x - x + A) function B) not a function 17) x2 + 5y2 = 1 A) function B) not a function 18) x + 4y = 2 A) function B) not a function 19) 2x + x2 - 37 = y A) function B) not a function Page 2 Copyright © 2015 Pearson Education, Inc Full file at https://TestbankDirect.eu/ Test Bank for Precalculus Concepts Through Functions A Unit Circle Approach to Trigonometry 3r Full file at https://TestbankDirect.eu/ Find the Value of a Function MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Find the value for the function 1) Find f(2) when f(x) = x2 + 5x - A) 10 B) 18 2) Find f(1) when f(x) = x2 - 5 x + A) - B) 3) Find f(-9) when f(x) = |x|- 6 A) 3 C) B) -15 4) Find f(5) when f(x) = x2 + 2x A) 35 B) 29 5) Find f(-x) when f(x) = -3x2 + 2x + A) -3x2 - 2x + B) 3x2 - 2x - 6) Find f(-x) when f(x) = A) D) -10 C) -2 D) C) 15 D) -3 C) D) 3 C) -3x2 - 2x - D) 3x2 - 2x + x x + 4 -x x + 4 B) -x x - 4 C) x -x + 4 D) -x -x2 + 4 7) Find -f(x) when f(x) = -2x2 + 5x + A) 2x2 - 5x - B) -2x2 - 5x + C) -2x2 - 5x - D) 2x2 - 5x + 8) Find -f(x) when f(x) = |x| + A) -|x| - B) |-x| + C) -|x| + D) |-x| - 9) Find f(x - 1) when f(x) = 3x2 - 3x - A) 3x2 - 9x + B) -9x2 + 3x + C) 3x2 - 9x - D) 3x2 - 12x - 10) Find f(x + 1) when f(x) = A) x2 + 2x - x - x2 - 8 x - B) x2 + 2x + x - C) x2 + 2x - x + 11) Find f(2x) when f(x) = 2x2 - 3x + A) 8x2 - 6x + B) 4x2 - 6x + C) 4x2 - 6x + 12) Find f(2x) when f(x) = 8x2 - 9x A) 32x2 - 18x B) 8x2 - 9x C) 16x2 - 18x Page 3 Copyright © 2015 Pearson Education, Inc Full file at https://TestbankDirect.eu/ D) x2 - x - D) 8x2 - 6x + D) 16x2 - 36x Test Bank for Precalculus Concepts Through Functions A Unit Circle Approach to Trigonometry 3r Full file13)atFind f(x + h) when f(x) = -2x https://TestbankDirect.eu/ + 2x - A) -2x2 - 4xh - 2h + 2x + 2h - C) -2x2 - 2h - 2x - 2h - 14) Find f(x + h) when f(x) = A) 5x + 5h + 4x + 4h - B) -2x2 - 2h + 2x + 2h - D) -2x2 - 2xh - 2h + 2x + 2h - 5x + 4x - B) 5x + 5h + 4x - C) 5x + 11h 4x - 3h D) 5x + 6h 4x - 7h Solve the problem 15) If f(x) = 4x3 + 2x2 - x + C and f(2) = 1, what is the value of C? A) C = -37 B) C = -9 C) C = 27 16) If f(x) = x - B , f(-9) = 0, and f(-4) is undefined, what are the values of A and B? x - A A) A = -4, B = -9 17) If f(x) = D) C = 43 B) A = -9, B = -4 C) A = 4, B = D) A = 9, B = C) A = -103 D) A = 103 x - 5A and f(10) = -10, what is the value of A? 10x + 5 A) A = 212 B) A = -212 18) If a rock falls from a height of 90 meters on Earth, the height H (in meters) after x seconds is approximately H(x) = 90 - 4.9x2 What is the height of the rock when x = 1.7 seconds? Round to the nearest hundredth, if necessary B) 104.16 m C) 81.67 m D) 76.13 m A) 75.84 m 19) If a rock falls from a height of 30 meters on Earth, the height H (in meters) after x seconds is approximately H(x) = 30 - 4.9x2 When does the rock strike the ground? Round to the nearest hundredth, if necessary A) 2.47 sec B) 6.12 sec C) 1.12 sec D) 1.25 sec Find the Domain of a Function Defined by an Equation MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Find the domain of the function 1) f(x) = -6x - A) all real numbers 2) f(x) = x2 + A) all real numbers 3) f(x) = B) {x|x ≥ 7} C) {x|x ≠ 0} D) {x|x > 0} B) {x|x ≥ -8} C) {x|x > -8} D) {x|x ≠ -8} B) {x|x ≠ -7} C) {x|x > -7} D) {x|x ≠ 0} B) {x|x ≠ 0} C) {x|x > 1} D) all real numbers x x2 + 7 A) all real numbers 4) g(x) = 3x x - 1 A) {x|x ≠ -1, 1} Page 4 Copyright © 2015 Pearson Education, Inc Full file at https://TestbankDirect.eu/ Test Bank for Precalculus Concepts Through Functions A Unit Circle Approach to Trigonometry 3r Full file at https://TestbankDirect.eu/ x - 4 5) h(x) = x3 - 81x A) {x|x ≠ -9, 0, 9} 6) f(x) = 21 - x A) {x|x ≤ 21} 7) B) {x|x ≠ 0} C) {x|x ≠ 4} D) all real numbers B) {x|x ≠ 21} C) {x|x ≤ 21} D) {x|x ≠ 21} B) {x|x ≥ 9} C) {x|x ≠ 9} D) all real numbers x x - 9 A) {x|x > 9} Form the Sum, Difference, Product, and Quotient of Two Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question For the given functions f and g, find the requested function and state its domain 1) f(x) = 7 - 6x; g(x) = -3x + Find f + g A) (f + g)(x) = -9x + 13; all real numbers B) (f + g)(x) = -3x + 7; {x| x ≠ } C) (f + g)(x) = 4x; all real numbers D) (f + g)(x) = -3x + 13; {x|x ≠ - 13 } A) (f - g)(x) = -5x - 5; all real numbers B) (f - g)(x) = -5x - 11; {x|x ≠ - 11 } C) (f - g)(x) = 9x - 11; {x|x ≠ 1} D) (f - g)(x) = 5x + 5; all real numbers 2) f(x) = 2x - 8; g(x) = 7x - Find f - g 3) f(x) = 5x + 4; g(x) = 3x - Find f · g A) (f · g)(x) = 15x2 - 28x - 32; all real numbers C) (f · g)(x) = 8x2 - 28x - 4; all real numbers B) (f · g)(x) = 15x2 + 4x - 32; {x|x ≠ -32} D) (f · g)(x) = 15x2 - 32; {x|x ≠ -32} 4) f(x) = 4x + 1; g(x) = 4x - 5 f Find g f 4x + A) ( )(x) = ; {x|x ≠ } g 4x - 5 f 4x + B) ( )(x) = ; {x|x ≠ - } g 4x - 5 f 4x - 5 C) ( )(x) = ; {x|x ≠ } g 4x + 1 f 4x - D) ( )(x) = ; {x|x ≠ - } g 4x + 5) f(x) = 16 - x2 ; g(x) = 4 - x Find f + g A) (f + g)(x) = -x2 + x + 12; all real numbers C) (f + g)(x) = -x2 - x + 20; {x|x ≠ 4, x ≠ -5} B) (f + g)(x) = 4 + x; {x|x ≠ -4} D) (f + g)(x) = x3 - 4x - 16x + 64; all real numbers Page 5 Copyright © 2015 Pearson Education, Inc Full file at https://TestbankDirect.eu/ Test Bank for Precalculus Concepts Through Functions A Unit Circle Approach to Trigonometry 3r Full file6)atf(x) = x + https://TestbankDirect.eu/ 1; g(x) = 5x2 Find f - g A) (f - g)(x) = -5x2 + x + 1; all real numbers C) (f - g)(x) = -5x2 + x + 1; {x|x ≠ -1} B) (f - g)(x) = 5x2 - x - 1; all real numbers D) (f - g)(x) = 5x2 + x + 1; all real numbers 7) f(x) = 4x3 + 3; g(x) = 6x2 - Find f · g A) (f · g)(x) = 24x5 - 4x3 + 18x2 - 3; all real numbers B) (f · g)(x) = 24x6 - 4x3 + 18x2 - 3; all real numbers C) (f · g)(x) = 24x5 - 4x3 + 18x2 - 3; {x|x ≠ 0} D) (f · g)(x) = 4x3 + 6x2 - 3; all real numbers 8) f(x) = x; g(x) = 4x - 5 f Find g x f ; {x|x ≥ 0, x ≠ } A) ( )(x) = 4x - 5 g f x B) ( )(x) = ; {x|x ≠ } 4x - 5 g x f ; {x|x ≠ 0} C) ( )(x) = 4x - 5 g f 4x - D) ( )(x) = ; {x|x ≥ 0} g x 9) f(x) = 2 - x; g(x) = x - 1 Find f · g A) (f · g)(x) = (2 - x)(x - 1); {x|1 ≤ x ≤ 2} C) (f · g)(x) = (2 - x)(x - 1); {x|x ≠ 1, x ≠ 2} 10) f(x) = B) (f · g)(x) = (2 - x)(x - 1); {x|x ≥ 0} D) (f · g)(x) = -x2 - 2; {x|x ≠ 2} 3x 7x + ; g(x) = 5x - 2 5x - 2 Find f - g A) (f - g)(x) = 4x + ; {x|x ≠ } 5x - 2 B) (f - g)(x) = 10x - ; {x|x ≠ } 5x - 2 C) (f - g)(x) = 4x + ; {x|x ≠ , x ≠ - } 5x - 2 D) (f - g)(x) = 4x + ; {x|x ≠ 0} 5x - 2 11) f(x) = x + 9; g(x) = x Find f · g A) (f · g)(x) = x + ; {x|x ≥ -9, x ≠ 0} x C) (f · g)(x) = 4x + 36 ; {x|x ≥ -9, x ≠ 0} x B) (f · g)(x) = 4x + 36 ; {x|x ≥ -9, x ≠ 0} x D) (f · g)(x) = 13 ; {x|x ≠ 0} x Solve the problem f x + , find the function g 12) Given f(x) = and ( )(x) = g x x + 7x A) g(x) = x + x + B) g(x) = x + x + C) g(x) = Page 6 Copyright © 2015 Pearson Education, Inc Full file at https://TestbankDirect.eu/ x - x - D) g(x) = x - x - Test Bank for Precalculus Concepts Through Functions A Unit Circle Approach to Trigonometry 3r Full file13)atExpress the gross salary G of a person who earns $ https://TestbankDirect.eu/ 15 per hour as a function of the number x of hours worked A) G(x) = 15x B) G(x) = 15 + x C) G(x) = 15 x D) G(x) = 15x2 14) Jacey, a commissioned salesperson, earns $360 base pay plus $36 per item sold. Express Jaceyʹs gross salary G as a function of the number x of items sold A) G(x) = 36x + 360 B) G(x) = 360x +36 C) G(x) = 36(x + 360) D) G(x) = 360(x + 36) Find and simplify the difference quotient of f, f(x + h) - f(x) , h ≠ 0, for the function h 15) f(x) = 6x + A) B) 6 + h C) 6 + 12(x + 2) h D) 16) f(x) = x2 + 5x - 2x2 + 2x + 2xh + h + h - h A) 2x+ h + 5 B) C) 2x+ h - D) 17) f(x) = A) 4x -1 4x (x + h) B) -1 x (x + h) C) 4x D) Solve the problem 18) Suppose that P(x) represents the percentage of income spent on leisure activites in year x and I(x) represents income in year x. Determine a function L that represents total leisure activites expenditures in year x I A) L(x) = (P · I)(x) B) L(x) = (P + I)(x) C) L(x) = (I - P)(x) D) L(x) = ( )(x) P 19) A retail store buys 120 VCRs from a distributor at a cost of $245 each plus an overhead charge of $40 per order The retail markup is 45% on the total price paid. Find the profit on the sale of one VCR A) $110.40 B) $11,040.00 C) $110.25 D) $110.10 Page 7 Copyright © 2015 Pearson Education, Inc Full file at https://TestbankDirect.eu/ Test Bank for Precalculus Concepts Through Functions A Unit Circle Approach to Trigonometry 3r Full at https://TestbankDirect.eu/ 1.2 file The Graph of a Function Identify the Graph of a Function MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x -axis, the y-axis, or the origin 1) y 10 -10 -5 10 x -5 -10 A) function domain: {x|x ≤ -1 or x ≥ 1} range: all real numbers intercepts: (-1, 0), (1, 0) symmetry: x-axis, y-axis, origin C) function domain: {x|-1 ≤ x ≤ 1} range: all real numbers intercepts: (-1, 0), (1, 0) symmetry: x-axis, y-axis B) function domain: all real numbers range: {y|y ≤ -1 or y ≥ 1} intercepts: (-1, 0), (1, 0) symmetry: y-axis D) not a function Page 8 Copyright © 2015 Pearson Education, Inc Full file at https://TestbankDirect.eu/ Test Bank for Precalculus Concepts Through Functions A Unit Circle Approach to Trigonometry 3r Full file2)at https://TestbankDirect.eu/ y -5 x -5 A) function domain: {x|x > 0} range: all real numbers intercept: (1, 0) symmetry: none C) function domain: all real numbers range: {y|y > 0} intercept: (1, 0) symmetry: none B) function domain: {x|x > 0} range: all real numbers intercept: (0, 1) symmetry: origin D) not a function 3) y - -3 - - 3 x -1 A) function domain: {x|-π ≤ x ≤ π} range: {y|-1 ≤ y ≤ 1} π π intercepts: (-π, 0), (- , 0), (0, 0), ( , 0), (π, 0) 2 B) function domain: {x|-1 ≤ x ≤ 1} range: {y|-π ≤ y ≤ π} π π intercepts: (-π, 0), (- , 0), (0, 0), ( , 0), (π, 0) 2 symmetry: origin C) function domain: all real numbers range: {y|-1 ≤ y ≤ 1} π π intercepts: (-π, 0), (- , 0), (0, 0), ( , 0), (π, 0) 2 symmetry: none D) not a function symmetry: origin Page 9 Copyright © 2015 Pearson Education, Inc Full file at https://TestbankDirect.eu/ Test Bank for Precalculus Concepts Through Functions A Unit Circle Approach to Trigonometry 3r Full file4)at https://TestbankDirect.eu/ y 10 -10 -5 10 x -5 -10 A) function domain: all real numbers range: {y|y ≤ 4} intercepts: (-3, 0), (0, 3), (1, 0) symmetry: none C) function domain: all real numbers range: {y|y ≤ 4} intercepts: (0, -3), (3, 0), (0, 1) symmetry: none B) function domain: {x|x ≤ 4} range: all real numbers intercepts: (-3, 0), (0, 3), (1, 0) symmetry: y-axis D) not a function 5) y 10 -10 -5 10 x -5 -10 A) function domain: {x|-7 ≤ x ≤ 7} range: {y|-7 ≤ y ≤ 7} intercepts: (-7, 0), (0, -7), (0, 7), (7, 0) symmetry: x-axis, y-axis, origin C) function domain: {x|-7 ≤ x ≤ 7} range: {y|-7 ≤ y ≤ 7} intercepts: (-7, 0), (0, -7), (0, 0), (0, 7), (7, 0) symmetry: origin B) function domain: {x|-7 ≤ x ≤ 7} range: {y|-7 ≤ y ≤ 7} intercepts: (-7, 0), (0, -7), (0, 7), (7, 0) symmetry: x-axis, y-axis D) not a function Page 10 Copyright © 2015 Pearson Education, Inc Full file at https://TestbankDirect.eu/ Test Bank for Precalculus Concepts Through Functions A Unit Circle Approach to Trigonometry 3r Full file at https://TestbankDirect.eu/ Match the correct function to the graph 12) y -6 -4 -2 x -2 -4 -6 A) y = -2x2 + 1 B) y = -2x2 C) y = -2x2 - 1 D) y = 1 - x2 Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function 13) The reflection of the graph of y = f(x) across the x-axis A) (2, -4) B) (-2, -4) C) (2, 4) D) (-2, 4) 14) The reflection of the graph of y = f(x) across the y-axis A) (-2, 4) B) (2, 4) C) (-2, -4) D) (2, -4) Find the function 15) Find the function that is finally graphed after the following transformations are applied to the graph of y = |x| The graph is shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and finally reflected across the x-axis B) y = -3|x - 3| - C) y = -(3|x + 3| - 2) D) y = 3|-x - 3| - A) y = -(3|x - 3| - 2) 16) Find the function that is finally graphed after the following transformations are applied to the graph of y = x The graph is shifted down 4 units, reflected about the x-axis, and finally shifted left 5 units B) y = - x + 5 + C) y = -x - 5 - D) y = - x - 5 + A) y = - x + 5 - 17) Find the function that is finally graphed after the following transformations are applied to the graph of y = x The graph is shifted up 6 units, reflected about the x-axis, and finally shifted left 5 units B) y = - ,x + - C) y = -x - + D) y = - ,x - - A) y = - ,x + + 1.6 Mathematical Models: Building Functions Build and Analyze Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Solve the problem 1) Elissa wants to set up a rectangular dog run in her backyard. She has 46 feet of fencing to work with and wants to use it all. If the dog run is to be x feet long, express the area of the dog run as a function of x B) A(x) = 24x - x2 C) A(x) = 25x2 - x D) A(x) = 22x - x2 A) A(x) = 23x - x2 2) Bob wants to fence in a rectangular garden in his yard. He has 90 feet of fencing to work with and wants to use it all. If the garden is to be x feet wide, express the area of the garden as a function of x A) A(x) = 45x - x2 B) A(x) = 46x - x2 C) A(x) = 47x2 - x D) A(x) = 44x - x2 Page 97 Copyright © 2015 Pearson Education, Inc Full file at https://TestbankDirect.eu/ Test Bank for Precalculus Concepts Through Functions A Unit Circle Approach to Trigonometry 3r Full file3)atSue wants to put a rectangular garden on her property using 84 https://TestbankDirect.eu/ meters of fencing. There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the rectangle. (Fencing is then needed only on the other three sides.) Let x represent the length of the side of the rectangle along the river. Express the gardenʹs area as a function of x 1 B) A(x) = 43x - 2x2 C) A(x) = 42x2 - x D) A(x) = 41x - x2 A) A(x) = 42x - x2 4) A farmer has 800 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width x of the rectangle. What is the domain of A? A) A(x) = -x2 + 400x; {x|0