NBT NBT Mathematics: Functions and Graphs 1 — Questions and Answers
Question 1: The function f(x) = 2x − 6. What is the x-intercept?
- x = 3 (Correct answer)
- x = −6
- x = −3
- x = 6
Correct answer: x = 3
Set f(x) = 0: 2x − 6 = 0 → x = 3.
Question 2: Which graph represents a decreasing linear function with a positive y-intercept?
- A straight line sloping downward from left to right, crossing the y-axis above the origin (Correct answer)
- A straight line sloping upward from left to right
- A parabola opening upwards
- A horizontal line above the x-axis
Correct answer: A straight line sloping downward from left to right, crossing the y-axis above the origin
A decreasing linear function has negative gradient; a positive y-intercept means it crosses the y-axis above zero.
Question 3: The quadratic function g(x) = x² − 4x + 3. What are the roots?
- x = 1 and x = 3 (Correct answer)
- x = −1 and x = −3
- x = 2 and x = −2
- x = 4 and x = 0
Correct answer: x = 1 and x = 3
Factorise: (x − 1)(x − 3) = 0, giving x = 1 or x = 3.
Question 4: What is the range of f(x) = x² + 1?
- y ≥ 1 (Correct answer)
- y ≥ 0
- all real numbers
- y ≤ 1
Correct answer: y ≥ 1
x² ≥ 0 for all x, so x² + 1 ≥ 1; minimum value is 1.
Question 5: The exponential function h(x) = 3^x. What is h(−2)?
- 1/9 (Correct answer)
- −9
- 9
- 1/3
Correct answer: 1/9
3^(−2) = 1 ÷ 3² = 1/9.
Question 6: For the parabola y = −2(x − 1)² + 8, what is the maximum value of y?
- 8 (Correct answer)
- 1
- −2
- 4
Correct answer: 8
The vertex is at (1, 8); since the coefficient is negative, y = 8 is the maximum.
Question 7: A graph of y = f(x) shows that f(2) = 5 and f(5) = −1. What is the average rate of change between x = 2 and x = 5?
- −2 (Correct answer)
- 2
- −6
- 6
Correct answer: −2
Average rate = (f(5) − f(2)) ÷ (5 − 2) = (−1 − 5) ÷ 3 = −6/3 = −2.
NBT NBT Mathematics: Functions and Graphs 1
The function f(x) = 2x − 6.
What is the x-intercept?