PRE CALCULUS Functions 5 — Questions and Answers
Question 1: What is the domain of f(x) = 1 / (x² - 9)?
- All real numbers except x = ±3 (Correct answer)
- All real numbers except x = 3
- x > 3
- All real numbers
Correct answer: All real numbers except x = ±3
The denominator x² - 9 = 0 when x = ±3, so those values are excluded from the domain.
Question 2: If f(x) = 5 - 2x, which equation represents f(f(x))?
- 4x - 5 (Correct answer)
- 4x + 5
- -4x + 5
- 4x - 10
Correct answer: 4x - 5
f(f(x)) = f(5 - 2x) = 5 - 2(5 - 2x) = 5 - 10 + 4x = 4x - 5.
Question 3: The graph of y = f(x) + 3 is the graph of y = f(x) shifted:
- Right 3 units
- Left 3 units
- Up 3 units (Correct answer)
- Down 3 units
Correct answer: Up 3 units
Adding a constant outside the function shifts the graph vertically upward by that amount.
Question 4: What is the range of f(x) = -x² + 5?
- y ≤ 5 (Correct answer)
- y ≥ 5
- All real numbers
- y ≤ -5
Correct answer: y ≤ 5
Since -x² ≤ 0 for all x, -x² + 5 ≤ 5, so the range is (-∞, 5].
Question 5: For the piecewise function f(x) = { x + 2 if x < 0; x² if x ≥ 0 }, what is f(-3) + f(2)?
- 3 (Correct answer)
- 5
- -1
- 7
Correct answer: 3
f(-3) = -3 + 2 = -1 (since -3 < 0) and f(2) = 2² = 4 (since 2 ≥ 0), so -1 + 4 = 3.
Question 6: Which of the following is the reflection of f(x) across the x-axis?
- -f(x) (Correct answer)
- f(-x)
- f(x) + 1
- 1/f(x)
Correct answer: -f(x)
Reflecting across the x-axis negates all output values, giving -f(x).
Question 7: If f(x) = √(4 - x²), what is the domain of f?
- -2 ≤ x ≤ 2 (Correct answer)
- x ≥ 2
- x ≤ 2
- x ≠ ±2
Correct answer: -2 ≤ x ≤ 2
We need 4 - x² ≥ 0, so x² ≤ 4, which gives -2 ≤ x ≤ 2.
PRE CALCULUS Functions 5
What is the domain of f(x) = 1 / (x² - 9)?