Order Precalculus Function Skills Assignment

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Order Precalculus Function Skills Assignment

Basic Function Concepts

1. Indicate whether the statement is true or false. Explain your reasoning.

(A) {(–4,5),(–1,5),(0,5),(5,5)} is a function.

(B) {(x, y) | y = 2x} is a function.

(C) If (4,a) and (4,b) are elements of a function, then a = b.

(D) The domain of a function is a subset of that function.

(E) In the function f = {(x,y) | y = 5x 3},y = f(x) is the image of x under f.

For questions 67 to 73, evaluate and simplify as indicated.

2. when f(x) = 28x – 10

68. y = f(–5) when f (x) = x

2 1

69. y = f(–1) when f (x) = 4x

5 2x

4 –3x

3 –5x

2 x 5

70. when

71. y = f(3) when

72. f(5x) when

73. f (x

2 1) when

For questions 74 to 78, find the domain, Df

, and range, Rf

Order Precalculus Function Skills Assignment

, for the given realvalued functions. Note: In a real-valued function both the domain and range of

the function consist of real numbers. All functions in this chapter are real-valued.

74. f defined by

75.

76. g defined by

77. h defined by h(x) = | 7x – 2 |

78. f defined by

Operations with Functions

For questions 79 to 82, using and g(x) = x

4

, write a simplified expression

for the indicated function. Refer to the following definitions, as needed.

For all real numbers x such that x ∈ Df ∩ Dg

:

(f g)(x) = f (x) g(x);

(f – g)(x) = f (x) – g(x);

(fg)(x) = f (x) · g(x); and

, where g(x) ≠ 0.

79. (f g)(x)

80. (f – g)(x)

81. (fg)(x)

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