PRE CALCULUS Functions 3 — Questions and Answers
Question 1: What does the horizontal line test determine?
- Whether a relation is a function
- Whether a function is one-to-one (Correct answer)
- Whether a function is even or odd
- Whether a function has an x-intercept
Correct answer: Whether a function is one-to-one
If every horizontal line intersects the graph at most once, the function is one-to-one and thus has an inverse.
Question 2: For f(x) = 3x + 6, what are the x- and y-intercepts?
- x-intercept: (-2, 0); y-intercept: (0, 6) (Correct answer)
- x-intercept: (2, 0); y-intercept: (0, 6)
- x-intercept: (0, 6); y-intercept: (-2, 0)
- x-intercept: (-2, 0); y-intercept: (0, -6)
Correct answer: x-intercept: (-2, 0); y-intercept: (0, 6)
Set f(x) = 0: 3x + 6 = 0 → x = -2; set x = 0: f(0) = 6.
Question 3: Which of the following represents an odd function?
- f(x) = x⁴ + 2
- f(x) = x³ - x (Correct answer)
- f(x) = x² + x
- f(x) = |x|
Correct answer: f(x) = x³ - x
f(-x) = (-x)³ - (-x) = -x³ + x = -(x³ - x) = -f(x), confirming f(x) = x³ - x is odd.
Question 4: If f(x) = x² - 4 and g(x) = x + 2, what is (f/g)(x) in simplified form?
- x - 2 (Correct answer)
- x + 2
- (x² - 4)/(x + 2)
- x² - 2
Correct answer: x - 2
f(x)/g(x) = (x² - 4)/(x + 2) = (x-2)(x+2)/(x+2) = x - 2, for x ≠ -2.
Question 5: What is the average rate of change of f(x) = x² on [2, 5]?
- 7 (Correct answer)
- 9
- 4
- 3
Correct answer: 7
Average rate of change = (f(5) - f(2))/(5 - 2) = (25 - 4)/3 = 21/3 = 7.
Question 6: If h(x) = f(g(x)) where f(x) = x + 1 and g(x) = x², what is h(3)?
- 10 (Correct answer)
- 7
- 16
- 4
Correct answer: 10
g(3) = 9, then f(9) = 9 + 1 = 10.
Question 7: Which function has a domain of all real numbers?
- f(x) = 1/x
- f(x) = √x
- f(x) = x³ - 5x (Correct answer)
- f(x) = log(x)
Correct answer: f(x) = x³ - 5x
Polynomials like x³ - 5x are defined for all real numbers, with no restrictions on x.
PRE CALCULUS Functions 3
What does the horizontal line test determine?