NBT Mathematics Functions and Calculus 1 — Questions and Answers
Question 1: What is the domain of f(x) = √(4 − x)?
- x ≤ 4 (Correct answer)
- x ≥ 4
- x < 4
- All real numbers
Correct answer: x ≤ 4
For the square root to be defined, the expression inside must be non-negative: 4 − x ≥ 0 gives x ≤ 4.
Question 2: What is the derivative of f(x) = 3x² − 2x + 5?
- 6x − 2 (Correct answer)
- 3x − 2
- 6x + 5
- 3x² − 2
Correct answer: 6x − 2
Using the power rule: the derivative of 3x² is 6x, the derivative of −2x is −2, and constants vanish, giving 6x − 2.
Question 3: What is lim(x→2) [(x² − 4) / (x − 2)]?
- 4 (Correct answer)
- 2
- 0
- Undefined
Correct answer: 4
Factoring gives (x+2)(x−2)/(x−2) = x+2; substituting x=2 yields 4.
Question 4: If f(x) = 2x + 1 and g(x) = x², what is f(g(3))?
- 19 (Correct answer)
- 13
- 37
- 7
Correct answer: 19
g(3) = 9, then f(9) = 2(9) + 1 = 19.
Question 5: The range of f(x) = −x² + 3 is:
- y ≤ 3 (Correct answer)
- y ≥ 3
- y ≤ −3
- All real numbers
Correct answer: y ≤ 3
The parabola opens downward with vertex at (0, 3), so the maximum output is 3 and f(x) ≤ 3 for all x.
Question 6: The gradient of the tangent to f(x) = x³ at x = 2 is:
- 12 (Correct answer)
- 8
- 6
- 3
Correct answer: 12
f′(x) = 3x², so f′(2) = 3(4) = 12.
Question 7: Which set of ordered pairs represents a function?
- {(1,2),(2,3),(3,4)} (Correct answer)
- {(1,2),(1,3),(2,4)}
- {(2,1),(2,2),(3,4)}
- {(1,2),(3,2),(1,5)}
Correct answer: {(1,2),(2,3),(3,4)}
A function requires each x-value to map to exactly one y-value; only {(1,2),(2,3),(3,4)} satisfies this.
NBT Mathematics Functions and Calculus 1
What is the domain of f(x) = √(4 − x)?