PRE CALCULUS Pre-Calculus Functions 3 — Questions and Answers
Question 1: Which of the following functions is odd?
- f(x) = x³ - x (Correct answer)
- f(x) = x² + 1
- f(x) = |x|
- f(x) = x² - x
Correct answer: f(x) = x³ - x
f(-x) = (-x)³ - (-x) = -x³ + x = -(x³ - x) = -f(x), confirming it is odd.
Question 2: The graph of y = f(2x) compared to y = f(x) is:
- Compressed horizontally by a factor of 2 (Correct answer)
- Stretched horizontally by a factor of 2
- Compressed vertically by a factor of 2
- Stretched vertically by a factor of 2
Correct answer: Compressed horizontally by a factor of 2
Replacing x with 2x compresses the graph horizontally by a factor of 2.
Question 3: If f(x) = 1/(x - 2), which value is NOT in the domain?
- x = 2 (Correct answer)
- x = 0
- x = -2
- x = 1
Correct answer: x = 2
The denominator equals zero when x = 2, making f undefined there.
Question 4: For f(x) = x² and g(x) = x + 3, what is (g ∘ f)(x)?
- x² + 3 (Correct answer)
- x² + 6x + 9
- (x + 3)²
- x³ + 3
Correct answer: x² + 3
(g ∘ f)(x) = g(f(x)) = g(x²) = x² + 3.
Question 5: What does the vertical line test determine?
- Whether a graph represents a function (Correct answer)
- Whether a function is even or odd
- Whether a function has an inverse
- Whether a function is continuous
Correct answer: Whether a graph represents a function
If any vertical line crosses a graph more than once, the graph does not represent a function.
Question 6: If f(x) = 2x + 4, what is f⁻¹(10)?
- 3 (Correct answer)
- 24
- 5
- 6
Correct answer: 3
f⁻¹(x) = (x - 4)/2, so f⁻¹(10) = (10 - 4)/2 = 3.
Question 7: Which transformation produces y = -f(x) from y = f(x)?
- Reflection over the x-axis (Correct answer)
- Reflection over the y-axis
- Vertical stretch by -1
- Horizontal reflection
Correct answer: Reflection over the x-axis
Multiplying the output by -1 reflects the graph across the x-axis.
PRE CALCULUS Pre-Calculus Functions 3
Which of the following functions is odd?