NBT NBT Mathematics: Functions and Graphs 4 — Questions and Answers
Question 1: The equation of a parabola is y = −(x + 1)² + 9. What are the x-intercepts?
- x = 2 and x = −4 (Correct answer)
- x = −2 and x = 4
- x = 1 and x = −9
- x = 3 and x = −3
Correct answer: x = 2 and x = −4
Set y = 0: (x + 1)² = 9 → x + 1 = ±3 → x = 2 or x = −4.
Question 2: f(x) = 3x − 2 and g(x) = x + 4. Where do f and g intersect?
- (3, 7) (Correct answer)
- (2, 6)
- (1, 5)
- (4, 8)
Correct answer: (3, 7)
Set 3x − 2 = x + 4 → 2x = 6 → x = 3; y = 3+4 = 7. Point: (3, 7).
Question 3: The graph of y = (1/2)^x compared to y = 2^x is:
- A reflection of y = 2^x in the y-axis (Correct answer)
- A reflection of y = 2^x in the x-axis
- A vertical shift of y = 2^x
- The same graph
Correct answer: A reflection of y = 2^x in the y-axis
(1/2)^x = 2^(−x), which is y = 2^x reflected in the y-axis.
Question 4: The function f(x) = x² − 2x − 8 has a minimum value at:
- x = 1, minimum y = −9 (Correct answer)
- x = −1, minimum y = −9
- x = 2, minimum y = −8
- x = 4, minimum y = 0
Correct answer: x = 1, minimum y = −9
Axis: x = 1; f(1) = 1 − 2 − 8 = −9. Minimum is (1, −9).
Question 5: A graph of f(x) is increasing for all x. Which could be f(x)?
- f(x) = 4^x (Correct answer)
- f(x) = (0.5)^x
- f(x) = −x + 3
- f(x) = −x²
Correct answer: f(x) = 4^x
4^x is an exponential function with base > 1, which always increases.
Question 6: The graph y = x² is translated 4 units to the right. What is the new equation?
- y = (x − 4)² (Correct answer)
- y = x² + 4
- y = (x + 4)²
- y = x² − 4
Correct answer: y = (x − 4)²
A horizontal shift right by 4 replaces x with (x − 4): y = (x − 4)².
Question 7: A straight line graph passes through A(−2, 4) and B(4, 1). What is its gradient?
- −1/2 (Correct answer)
- 1/2
- −2
- 2
Correct answer: −1/2
m = (1 − 4) ÷ (4 − (−2)) = −3 ÷ 6 = −1/2.
NBT NBT Mathematics: Functions and Graphs 4
The equation of a parabola is y = −(x + 1)² + 9.
What are the x-intercepts?