PRE CALCULUS Pre-Calculus Functions 5 — Questions and Answers
Question 1: Which statement about the composition (f ∘ g)(x) is always true?
- The domain of f ∘ g is a subset of the domain of g (Correct answer)
- f ∘ g = g ∘ f for all functions
- The range of f ∘ g equals the range of f
- f ∘ g is defined whenever g is defined
Correct answer: The domain of f ∘ g is a subset of the domain of g
The domain of f ∘ g consists of all x in the domain of g such that g(x) is in the domain of f.
Question 2: For f(x) = 2|x - 1| - 3, what is the minimum value of f?
- -3 (Correct answer)
- -1
- 0
- 2
Correct answer: -3
The absolute value term is minimized at x = 1, giving f(1) = 0 - 3 = -3.
Question 3: If f is an even function and f(3) = 7, what is f(-3)?
- 7 (Correct answer)
- -7
- 3
- -3
Correct answer: 7
Even functions satisfy f(-x) = f(x), so f(-3) = f(3) = 7.
Question 4: The function f(x) = x³ is stretched vertically by a factor of 4. The new function is:
- 4x³ (Correct answer)
- x³/4
- (4x)³
- (x/4)³
Correct answer: 4x³
A vertical stretch by factor 4 multiplies the output: new function = 4·f(x) = 4x³.
Question 5: Which pair of functions are inverses of each other?
- f(x) = 2x + 3 and g(x) = (x - 3)/2 (Correct answer)
- f(x) = x² and g(x) = x/2
- f(x) = x + 5 and g(x) = x - 3
- f(x) = 3x and g(x) = 3x
Correct answer: f(x) = 2x + 3 and g(x) = (x - 3)/2
Composing them: f(g(x)) = 2·(x-3)/2 + 3 = x - 3 + 3 = x, confirming they are inverses.
Question 6: What is the y-intercept of f(x) = 3x² - 2x + 5?
- 5 (Correct answer)
- 3
- -2
- 0
Correct answer: 5
The y-intercept is f(0) = 3(0)² - 2(0) + 5 = 5.
Question 7: If f(x) = x/(x² - 9), which values are excluded from the domain?
- x = 3 and x = -3 (Correct answer)
- x = 0 only
- x = 9 and x = -9
- x = 3 only
Correct answer: x = 3 and x = -3
x² - 9 = 0 when x = ±3, so both values must be excluded from the domain.
PRE CALCULUS Pre-Calculus Functions 5
Which statement about the composition (f ∘ g)(x) is always true?