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Review Questions
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10.1 Characteristics of a Function
 
10.2 Evaluating Functions
 
10.3 Compound Functions
 
10.4 Inverse Functions
 
10.5 Domain and Range
 
 
10.6 Graphing Functions
 
10.7 Identifying the Graphs of Polynomial Functions
 
10.8 Review Questions
 
10.9 Explanations
 
Review Questions
1. f(x) = ax and g(x) = bx. If fg(x) = 5x2 + 2, what is ab?
(A) ab = 5x
(B) ab = 5x +
(C) ab = x2
(D) ab = 7x
(E) Impossible to tell
2. If f(x) = 2x and g(x) = , what is f–1(g–1(2))?
(A) 0
(B)
(C) 1
(D)
(E) 2
3. If f(x) = 2x – 3, g(x) = x + 1, h(x) = 3x, and g(f(3)) – h(x) = 1, what is x?
(A) 0
(B) .5
(C) 1
(D) 1.5
(E) 2
4. Which of the following lines are asymptotes of the graph y = 2?
  I. x = 2
 II. y = 2
III. y = 0
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III
5. A portion of the graph of y = f(x) is shown in the figure below. Which of the following could be f(x)?
(A) x4 + ax3 + bx2 + cx
(B) x4 + ax2 + b
(C) –x4 + ax3 + bx2 + cx + d
(D) x3 + ax2 + bx + c
(E) x4 + b2x2 + c2
6. Suppose f(x) = –f(–x). Which of the following could be the graph of y = f(x)?
(A)
(B)
(C)
(D)
(E)
7. What is the maximum value of the function f(x) = 10 – 2(x – 3)(x + 3)?
(A) –28
(B) –8
(C) 0
(D) 8
(E) 28
8. If f: (x, y) = (x – y, x + y) for every pair (x, y) in the plane, for what points (x, y) is it true that (x, y) = (x, y)?
(A) (0, 0) only
(B) The set of points (x, y) such that x = 0
(C) The set of points (x, y) such that y = 0
(D) The set of points (x, y) such that x = y
(E) The set of points (x, y) such that 2x = y
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