216 CHAPTER 2 Graphs and Functions Decide whether each relation defines v as a function of x. Give the domain and ranser See Example 5. 34. y=x 35. x = y° 33. y= x2 37.) y = 2x- 5 38. у 3D - 6х + 4 36. х 3D уч 40. x-y< 4 41. y = Vx 39 x+y<3 39. x+ 42. y = -Vx 43. xy 2 44. xy = -6 45. y = V4x + 1 46. y = V7- 2x -7 48. y = 47. y = 49. Concept Check Choose the correct answer: For function f, the notation f(3) means A. the variable f times 3, or 3f. B. the value of the dependent variable when the independent variable is 3. C. the value of the independent variable when the dependent variable is 3. D. f equals 3. 50. Concept Check Give an example of a function from everyday life. (Hint: Fill in the blanks: ..) depends on is a function of so Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. %3D Sf(0) 52. f(-3) 53. g(-2) 54. g(10) 55. 56. 3 () 58. 8 4 57. g f(p) 60. g(k) 61. f(-x) 62. g(-x) 63. f(x + 2) 64. f(a + 4) 65) f(2m – 3) 66. f(3t – 2) For each function, find (a) f(2) and (b) f(-1). See Example 7. 67) f = {(-1, 3), (4, 7), (0, 6), (2, 2)} 68. ƒ = {(2,5), (3, 9), (–1, 11), (5, 3)} %3D 69 70. 10 15 5 3 19 -1 27 3 20 71. 72. y = f(x) -2 0 4 y = f(x) 217 2.3 Functions Use the graph of y = f(x) to find each function value: (a) ƒ(-2), (b) f(0), (c) f(1) and (d) f(4). See Example 7(d). 73. 74. 2. 3. 4. 75. 76. 4 4. 2-1- 2-3-4 -2-1-0 2-3-4 An equation that defines y as a function of x is given. (a) Rewrite each equation using function notation f(x). (b) Find f(3). See Example 8. x + 3y = 12 78. x - 4y = 8 79. у + 2x23D 3 — х 80. y – 3x² = 2 + x 81. 4x – 3y = 8 82. -2x + 5y = 9 Concept Check Answer each question. 83. If (3, 4) is on the graph of y = f(x), which one of the following must be true: f(3) = 4 or f(4) = 3? %3D %3| 84. The figure shows a portion of the graph of f(x) = x² + 3x + 1 %3D and a rectangle with its base on the x-axis and a vertex on the graph. What is the area of the rectangle? (Hint: f(0.2) is the height.) y = f(x) 0.2 0.3 85. The graph of y, = f(x) is shown with a display at the bottom. What is f(3)? 86. The graph of y, = f(x) is shown with a display at the bottom. What is f(-2)? %3D %3D NORMAL FLOAT AUTO REAL RADIAN MP NORMAL FLOAT AUTO REAL RADIAN MP Y1= (X+2)2-3 10 Y1=abs(X-3)-4 10 10-++ +++ 10 + 4+10 -10 X#3

216 CHAPTER 2 Graphs and Functions Decide whether each relation defines v as a function of x. Give the domain and ranser See Example 5. 34. y=x 35. x = y° 33. y= x2 37.) y = 2x- 5 38. у 3D - 6х + 4 36. х 3D уч 40. x-y< 4 41. y = Vx 39 x+y<3 39. x+ 42. y = -Vx 43. xy 2 44. xy = -6 45. y = V4x + 1 46. y = V7- 2x -7 48. y = 47. y = 49. Concept Check Choose the correct answer: For function f, the notation f(3) means A. the variable f times 3, or 3f. B. the value of the dependent variable when the independent variable is 3. C. the value of the independent variable when the dependent variable is 3. D. f equals 3. 50. Concept Check Give an example of a function from everyday life. (Hint: Fill in the blanks: ..) depends on is a function of so Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. %3D Sf(0) 52. f(-3) 53. g(-2) 54. g(10) 55. 56. 3 () 58. 8 4 57. g f(p) 60. g(k) 61. f(-x) 62. g(-x) 63. f(x + 2) 64. f(a + 4) 65) f(2m – 3) 66. f(3t – 2) For each function, find (a) f(2) and (b) f(-1). See Example 7. 67) f = {(-1, 3), (4, 7), (0, 6), (2, 2)} 68. ƒ = {(2,5), (3, 9), (–1, 11), (5, 3)} %3D 69 70. 10 15 5 3 19 -1 27 3 20 71. 72. y = f(x) -2 0 4 y = f(x) 217 2.3 Functions Use the graph of y = f(x) to find each function value: (a) ƒ(-2), (b) f(0), (c) f(1) and (d) f(4). See Example 7(d). 73. 74. 2. 3. 4. 75. 76. 4 4. 2-1- 2-3-4 -2-1-0 2-3-4 An equation that defines y as a function of x is given. (a) Rewrite each equation using function notation f(x). (b) Find f(3). See Example 8. x + 3y = 12 78. x - 4y = 8 79. у + 2x23D 3 — х 80. y – 3x² = 2 + x 81. 4x – 3y = 8 82. -2x + 5y = 9 Concept Check Answer each question. 83. If (3, 4) is on the graph of y = f(x), which one of the following must be true: f(3) = 4 or f(4) = 3? %3D %3| 84. The figure shows a portion of the graph of f(x) = x² + 3x + 1 %3D and a rectangle with its base on the x-axis and a vertex on the graph. What is the area of the rectangle? (Hint: f(0.2) is the height.) y = f(x) 0.2 0.3 85. The graph of y, = f(x) is shown with a display at the bottom. What is f(3)? 86. The graph of y, = f(x) is shown with a display at the bottom. What is f(-2)? %3D %3D NORMAL FLOAT AUTO REAL RADIAN MP NORMAL FLOAT AUTO REAL RADIAN MP Y1= (X+2)2-3 10 Y1=abs(X-3)-4 10 10-++ +++ 10 + 4+10 -10 X#3

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.7: Operations On Functions

Problem 63E

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