UTMA Functions and Graphing 2 — Questions and Answers
Question 1: What are the x-intercepts of f(x) = x² − 5x + 6?
- x = 2 and x = 3 (Correct answer)
- x = −2 and x = −3
- x = 1 and x = 6
- x = −1 and x = 6
Correct answer: x = 2 and x = 3
Factoring gives (x − 2)(x − 3) = 0, so x = 2 and x = 3.
Question 2: Which of the following is a one-to-one function?
- f(x) = 2x + 5 (Correct answer)
- f(x) = x²
- f(x) = |x|
- f(x) = sin x
Correct answer: f(x) = 2x + 5
A linear function f(x) = 2x + 5 passes the horizontal line test, confirming it is one-to-one.
Question 3: What is the y-intercept of f(x) = (x + 3)(x − 1)?
- −3 (Correct answer)
- 3
- 1
- −1
Correct answer: −3
Setting x = 0 gives f(0) = (3)(−1) = −3.
Question 4: If f(x) = x² and g(x) = x + 1, what is (f + g)(2)?
- 7 (Correct answer)
- 9
- 5
- 6
Correct answer: 7
(f + g)(2) = f(2) + g(2) = 4 + 3 = 7.
Question 5: The function f(x) = 1/(x − 4) has a vertical asymptote at:
- x = 4 (Correct answer)
- x = −4
- y = 0
- y = 4
Correct answer: x = 4
A vertical asymptote occurs where the denominator equals zero: x − 4 = 0 gives x = 4.
Question 6: Which transformation produces the graph of y = −f(x)?
- Reflection over the x-axis (Correct answer)
- Reflection over the y-axis
- Shift downward
- Vertical stretch
Correct answer: Reflection over the x-axis
Multiplying the output by −1 reflects the graph over the x-axis.
Question 7: For f(x) = |x − 2|, what is the vertex (minimum point) of the graph?
- (2, 0) (Correct answer)
- (0, 2)
- (−2, 0)
- (0, −2)
Correct answer: (2, 0)
The absolute value expression equals zero when x = 2, giving the vertex at (2, 0).
UTMA Functions and Graphing 2
What are the x-intercepts of f(x) = x² − 5x + 6?