NBT NBT Algebra and Functions 4 — Questions and Answers
Question 1: If f(x) = 2x² − 3x + 1, what is f(−2)?
- 15 (Correct answer)
- 11
- 3
- −1
Correct answer: 15
f(−2) = 2(4) − 3(−2) + 1 = 8 + 6 + 1 = 15.
Question 2: Which value of x satisfies |2x − 5| = 9?
- x = 7 or x = −2 (Correct answer)
- x = 7 only
- x = −2 only
- x = 2 or x = −7
Correct answer: x = 7 or x = −2
2x − 5 = 9 gives x = 7, and 2x − 5 = −9 gives x = −2.
Question 3: A function g satisfies g(2) = 5 and g(x + 1) = g(x) + 3 for all x. What is g(5)?
- 14 (Correct answer)
- 11
- 17
- 8
Correct answer: 14
g(3) = 8, g(4) = 11, g(5) = 14 by applying the recurrence three times.
Question 4: What is the range of f(x) = −x² + 4?
- (−∞, 4] (Correct answer)
- [4, ∞)
- (−∞, ∞)
- [−4, 4]
Correct answer: (−∞, 4]
The parabola opens downward with vertex at (0, 4), so f(x) ≤ 4 for all x.
Question 5: If 3^(x+1) = 81, what is x?
- 3 (Correct answer)
- 4
- 2
- 27
Correct answer: 3
81 = 3⁴, so x + 1 = 4, giving x = 3.
Question 6: Two lines are perpendicular. One has slope 2/3. What is the slope of the other?
- −3/2 (Correct answer)
- 3/2
- −2/3
- 2/3
Correct answer: −3/2
Perpendicular slopes are negative reciprocals: −1 ÷ (2/3) = −3/2.
Question 7: Which inequality represents the solution to −4x + 3 > 11?
- x < −2 (Correct answer)
- x > −2
- x < 2
- x > 2
Correct answer: x < −2
−4x > 8 → x < −2 (inequality flips when dividing by a negative).
NBT NBT Algebra and Functions 4
If f(x) = 2x² − 3x + 1, what is f(−2)?