IMSA Functions and Graphing 2 — Questions and Answers
Question 1: Which of the following is a linear function?
- f(x) = 2x + 5 (Correct answer)
- f(x) = x²
- f(x) = √x
- f(x) = 1/x
Correct answer: f(x) = 2x + 5
f(x) = 2x + 5 is linear because the variable x has an exponent of 1.
Question 2: What are the coordinates of the vertex of y = (x − 2)² + 3?
- (2, 3) (Correct answer)
- (−2, 3)
- (2, −3)
- (3, 2)
Correct answer: (2, 3)
In vertex form y = (x − h)² + k, the vertex is at (h, k), so here it is (2, 3).
Question 3: If g(x) = 4x − 7 and g(x) = 9, what is x?
- 4 (Correct answer)
- 2.5
- 16
- −0.5
Correct answer: 4
4x − 7 = 9 gives 4x = 16, so x = 4.
Question 4: What is the y-value when x = −1 on the graph of y = x³?
- −1 (Correct answer)
- 1
- −3
- 3
Correct answer: −1
y = (−1)³ = −1.
Question 5: A function f(x) is even if:
- f(−x) = f(x) for all x (Correct answer)
- f(−x) = −f(x) for all x
- f(0) = 0
- f(x) > 0 for all x
Correct answer: f(−x) = f(x) for all x
An even function satisfies f(−x) = f(x), meaning it is symmetric about the y-axis.
Question 6: On a graph, a horizontal line y = 4 intersects y = 2x − 2 at what x-value?
- 3 (Correct answer)
- 2
- 6
- 1
Correct answer: 3
Setting 2x − 2 = 4 gives 2x = 6, so x = 3.
IMSA Functions and Graphing 2
Which of the following is a linear function?