NBT NBT Mathematics: Functions and Graphs 5 — Questions and Answers
Question 1: For f(x) = 2x² − 3x + 1, evaluate f(−1).
- 6 (Correct answer)
- −4
- 0
- 4
Correct answer: 6
f(−1) = 2(1) − 3(−1) + 1 = 2 + 3 + 1 = 6.
Question 2: The graph of y = f(x) has y-intercept (0, −4) and x-intercepts at x = −1 and x = 4. Which equation is consistent?
- y = (x + 1)(x − 4) (Correct answer)
- y = −(x + 1)(x − 4)
- y = (x − 1)(x + 4)
- y = (x + 1)(x + 4)
Correct answer: y = (x + 1)(x − 4)
At x = 0: (0+1)(0−4) = −4 ✓. So y = (x+1)(x−4) gives y-intercept −4 and roots −1 and 4.
Question 3: What transformation maps y = x² onto y = 3x²?
- Vertical stretch by factor 3 (Correct answer)
- Vertical compression by factor 3
- Horizontal stretch by factor 3
- Vertical shift up by 3
Correct answer: Vertical stretch by factor 3
Multiplying x² by 3 stretches the graph vertically by a factor of 3.
Question 4: The function f(x) = −3^x is:
- Always negative (Correct answer)
- Always positive
- Sometimes zero
- Increasing for all x
Correct answer: Always negative
3^x > 0 for all x, so −3^x < 0 for all x — always negative.
Question 5: A linear function f passes through (−3, 0) and has gradient 2. What is f(4)?
- 14 (Correct answer)
- 8
- 11
- 10
Correct answer: 14
y = 2(x + 3); f(4) = 2(7) = 14.
Question 6: The diagram shows g(x) = k · 2^x passing through (2, 12). What is k?
- 3 (Correct answer)
- 6
- 4
- 2
Correct answer: 3
12 = k · 2² = 4k → k = 3.
Question 7: For which value of x does 2^x = 1/8?
- x = −3 (Correct answer)
- x = 3
- x = −1/3
- x = 1/3
Correct answer: x = −3
1/8 = 2^(−3), so 2^x = 2^(−3) → x = −3.
NBT NBT Mathematics: Functions and Graphs 5
For f(x) = 2x² − 3x + 1, evaluate f(−1).