IMSA Functions and Graphing 1 — Questions and Answers
Question 1: Which of the following represents a function?
- Each input has exactly one output (Correct answer)
- One input can have multiple outputs
- Each output must equal its input
- Inputs and outputs are always equal
Correct answer: Each input has exactly one output
A function requires that every input (x-value) maps to exactly one output (y-value).
Question 2: What is the domain of f(x) = 1/(x − 3)?
- All real numbers except x = 3 (Correct answer)
- All real numbers
- x > 3 only
- x ≥ 3
Correct answer: All real numbers except x = 3
The function is undefined when the denominator equals zero, i.e., when x = 3.
Question 3: If f(x) = x² − 4, what is f(−2)?
- 0 (Correct answer)
- −8
- 4
- 8
Correct answer: 0
f(−2) = (−2)² − 4 = 4 − 4 = 0.
Question 4: What is the range of f(x) = |x|?
- y ≥ 0 (Correct answer)
- All real numbers
- y > 0
- y ≤ 0
Correct answer: y ≥ 0
The absolute value function always produces non-negative results, so the range is y ≥ 0.
Question 5: What does the graph of y = x² look like?
- A parabola opening upward (Correct answer)
- A straight line
- A parabola opening downward
- A circle
Correct answer: A parabola opening upward
y = x² is a quadratic equation whose graph is a U-shaped parabola opening upward.
Question 6: For the function y = 3x − 1, what is the output when the input is 4?
- 11 (Correct answer)
- 13
- 9
- 3
Correct answer: 11
y = 3(4) − 1 = 12 − 1 = 11.
IMSA Functions and Graphing 1
Which of the following represents a function?