PRE CALCULUS Pre-Calculus Functions 2 — Questions and Answers
Question 1: Which of the following best describes an even function?
- f(-x) = f(x) for all x in the domain (Correct answer)
- f(-x) = -f(x) for all x in the domain
- f(x) = f(x+2) for all x
- f(x) > 0 for all x
Correct answer: f(-x) = f(x) for all x in the domain
An even function satisfies f(-x) = f(x), meaning it is symmetric about the y-axis.
Question 2: If f(x) = x² - 4 and g(x) = 2x + 1, what is (f ∘ g)(0)?
- -3 (Correct answer)
- 1
- 5
- -4
Correct answer: -3
g(0) = 1, then f(1) = 1 - 4 = -3.
Question 3: What is the inverse of f(x) = 3x - 6?
- f⁻¹(x) = (x + 6)/3 (Correct answer)
- f⁻¹(x) = (x - 6)/3
- f⁻¹(x) = 3x + 6
- f⁻¹(x) = x/3 - 6
Correct answer: f⁻¹(x) = (x + 6)/3
Swap x and y then solve: x = 3y - 6 → y = (x + 6)/3.
Question 4: Which transformation shifts the graph of f(x) down by 5 units?
- f(x) - 5 (Correct answer)
- f(x - 5)
- f(x) + 5
- f(x + 5)
Correct answer: f(x) - 5
Subtracting 5 outside the function shifts the graph down 5 units.
Question 5: A function f has f(2) = 7 and f(5) = 7. Which property does this NOT necessarily imply?
- f is one-to-one (Correct answer)
- f is defined at x = 2
- f is defined at x = 5
- f maps integers to integers
Correct answer: f is one-to-one
A one-to-one function cannot have two different inputs mapping to the same output, but f(2) = f(5) = 7 shows this function is not one-to-one.
Question 6: What is the range of f(x) = |x| + 2?
- [2, ∞) (Correct answer)
- (-∞, ∞)
- [0, ∞)
- (-∞, 2]
Correct answer: [2, ∞)
|x| ≥ 0 for all x, so |x| + 2 ≥ 2, making the range [2, ∞).
Question 7: If f(x) = √(x - 3), what is the domain of f?
- [3, ∞) (Correct answer)
- (-∞, 3]
- (3, ∞)
- All real numbers
Correct answer: [3, ∞)
The expression under the radical must be non-negative: x - 3 ≥ 0, so x ≥ 3.
PRE CALCULUS Pre-Calculus Functions 2
Which of the following best describes an even function?