College Math Placement Test Functions 5 — Questions and Answers
Question 1: What is the average rate of change of f(x) = x² + 2x from x = 1 to x = 4?
- 5
- 7 (Correct answer)
- 9
- 11
Correct answer: 7
Average rate of change = [f(4) - f(1)] / (4-1) = [(16+8) - (1+2)] / 3 = 21/3 = 7.
Question 2: If f(x) = log₂(x), then f(32) equals:
- 4
- 5 (Correct answer)
- 6
- 16
Correct answer: 5
log₂(32) = log₂(2⁵) = 5.
Question 3: The function f(x) = -2(x - 1)² + 8 has a maximum value of:
- 1
- 8 (Correct answer)
- -2
- 6
Correct answer: 8
Since a = -2 < 0 the parabola opens downward, and the vertex at (1, 8) gives the maximum value of 8.
Question 4: Which of the following pairs of functions are inverses of each other?
- f(x) = 2x and g(x) = x/2 + 1
- f(x) = x + 5 and g(x) = x - 5 (Correct answer)
- f(x) = 3x and g(x) = x + 3
- f(x) = x² and g(x) = x²
Correct answer: f(x) = x + 5 and g(x) = x - 5
f(g(x)) = (x-5)+5 = x and g(f(x)) = (x+5)-5 = x, confirming they are inverses.
Question 5: If f(x) = x/(x-2), what happens to f(x) as x approaches 2?
- f(x) approaches 0
- f(x) approaches 1
- f(x) approaches infinity (Correct answer)
- f(x) approaches -2
Correct answer: f(x) approaches infinity
As x → 2, the denominator approaches 0 while the numerator approaches 2, so f(x) → ±∞.
Question 6: Which transformation of f(x) results in a vertical stretch by a factor of 3?
- f(3x)
- f(x/3)
- 3f(x) (Correct answer)
- f(x) + 3
Correct answer: 3f(x)
Multiplying the entire function output by 3, written as 3f(x), produces a vertical stretch by factor 3.
Question 7: Given that f is a linear function with f(0) = -4 and f(3) = 2, find f(6).
- 6
- 8 (Correct answer)
- 10
- 12
Correct answer: 8
Slope = (2-(-4))/(3-0) = 2, so f(x) = 2x - 4, and f(6) = 12 - 4 = 8.
College Math Placement Test Functions 5
What is the average rate of change of f(x) = x² + 2x from x = 1 to x = 4?