College Math Placement Test Functions 2 — Questions and Answers
Question 1: If f(x) = 2x² - 3x + 1, what is f(-2)?
- 15 (Correct answer)
- 11
- 3
- -3
Correct answer: 15
f(-2) = 2(4) - 3(-2) + 1 = 8 + 6 + 1 = 15.
Question 2: Which of the following represents a one-to-one function?
- f(x) = x²
- f(x) = |x|
- f(x) = x³ (Correct answer)
- f(x) = sin(x)
Correct answer: f(x) = x³
f(x) = x³ is one-to-one because each output corresponds to exactly one input; the others fail the horizontal line test.
Question 3: Given g(x) = √(x - 4), what is the domain of g?
- x ≥ 0
- x > 4
- x ≥ 4 (Correct answer)
- All real numbers
Correct answer: x ≥ 4
The radicand x - 4 must be ≥ 0, so x ≥ 4.
Question 4: If h(x) = 3x - 5 and h(a) = 7, what is the value of a?
- 2
- 4 (Correct answer)
- 6
- 12
Correct answer: 4
3a - 5 = 7 → 3a = 12 → a = 4.
Question 5: Which graph best represents a function with range [0, ∞)?
- A line through the origin with slope 1
- A parabola opening upward with vertex at (0,0) (Correct answer)
- A circle centered at the origin
- A horizontal line at y = -1
Correct answer: A parabola opening upward with vertex at (0,0)
A parabola opening upward with vertex at (0,0) has all y-values ≥ 0, giving range [0, ∞).
Question 6: If f(x) = 5x + 2 and g(x) = x - 3, what is (f ∘ g)(x)?
- 5x - 13 (Correct answer)
- 5x - 1
- 5x + 5
- 5x² - 13x - 6
Correct answer: 5x - 13
f(g(x)) = f(x-3) = 5(x-3) + 2 = 5x - 15 + 2 = 5x - 13.
Question 7: A function f is defined so that f(2) = 7 and f(5) = 13. If f is linear, what is f(8)?
- 17
- 19 (Correct answer)
- 21
- 25
Correct answer: 19
The slope is (13-7)/(5-2) = 2, so f(x) = 2x + 3, and f(8) = 16 + 3 = 19.
College Math Placement Test Functions 2
If f(x) = 2x² - 3x + 1, what is f(-2)?