PRE CALCULUS Pre-Calculus Functions 4 — Questions and Answers
Question 1: A function f is one-to-one. Which tool best verifies this from its graph?
- Horizontal line test (Correct answer)
- Vertical line test
- Domain check
- Range check
Correct answer: Horizontal line test
If every horizontal line crosses the graph at most once, the function is one-to-one.
Question 2: What is the period of f(x) = sin(3x)?
- 2π/3 (Correct answer)
- 3π
- 6π
- 2π
Correct answer: 2π/3
The period of sin(bx) is 2π/b, so for b = 3 the period is 2π/3.
Question 3: If f(x) = x² and g(x) = √x (x ≥ 0), then (f ∘ g)(x) simplifies to:
- x (Correct answer)
- x²
- √x
- |x|
Correct answer: x
f(g(x)) = f(√x) = (√x)² = x for x ≥ 0.
Question 4: The graph of f(x) = (x - 3)² + 1 has its vertex at:
- (3, 1) (Correct answer)
- (-3, 1)
- (3, -1)
- (-3, -1)
Correct answer: (3, 1)
In vertex form f(x) = (x - h)² + k, the vertex is (h, k) = (3, 1).
Question 5: Which function has a vertical asymptote at x = -4?
- f(x) = 1/(x + 4) (Correct answer)
- f(x) = 1/(x - 4)
- f(x) = x + 4
- f(x) = (x + 4)²
Correct answer: f(x) = 1/(x + 4)
The denominator x + 4 equals zero at x = -4, creating a vertical asymptote there.
Question 6: If f(x) = 5x - 2 and f(a) = 13, what is a?
- 3 (Correct answer)
- 63
- 2.2
- 11
Correct answer: 3
5a - 2 = 13 → 5a = 15 → a = 3.
Question 7: What is the domain of f(x) = ln(x - 1)?
- (1, ∞) (Correct answer)
- [1, ∞)
- (-∞, 1)
- All real numbers
Correct answer: (1, ∞)
The natural log requires a positive argument: x - 1 > 0, so x > 1.
PRE CALCULUS Pre-Calculus Functions 4
A function f is one-to-one.
Which tool best verifies this from its graph?