NBT NBT Mathematics: Functions and Graphs 3 — Questions and Answers
Question 1: The line y = mx + c has gradient −3 and passes through (1, 2). What is the equation?
- y = −3x + 5 (Correct answer)
- y = −3x − 5
- y = 3x − 1
- y = −3x + 2
Correct answer: y = −3x + 5
Using y − 2 = −3(x − 1): y = −3x + 3 + 2 = −3x + 5.
Question 2: A parabola has equation y = 2x² − 8x + 6. The axis of symmetry is:
- x = 2 (Correct answer)
- x = −2
- x = 4
- x = 1
Correct answer: x = 2
Axis of symmetry: x = −b/(2a) = 8/(2×2) = 2.
Question 3: The graph of f(x) = 2^x is reflected in the y-axis. What is the equation of the reflected graph?
- f(x) = 2^(−x) (Correct answer)
- f(x) = −2^x
- f(x) = 2^x − 1
- f(x) = (1/2)^(−x)
Correct answer: f(x) = 2^(−x)
Reflection in y-axis replaces x with −x: f(x) = 2^(−x).
Question 4: On a graph, f(x) is a straight line that is neither increasing nor decreasing. Which type of function is this?
- Constant function (Correct answer)
- Linear function with positive gradient
- Quadratic function
- Exponential function
Correct answer: Constant function
A horizontal line represents a constant function where the output is the same for all x.
Question 5: Which function has an asymptote at y = 2?
- f(x) = 3^x + 2 (Correct answer)
- f(x) = x² + 2
- f(x) = 2x + 1
- f(x) = 2x²
Correct answer: f(x) = 3^x + 2
Exponential functions of the form a^x + c have horizontal asymptote y = c; here y = 2.
Question 6: The function f(x) = −x² + 4. For what values of x is f(x) > 0?
- −2 < x < 2 (Correct answer)
- x < −2 or x > 2
- x > 0
- x < 0
Correct answer: −2 < x < 2
−x² + 4 > 0 → x² < 4 → −2 < x < 2.
Question 7: A graph shows y = f(x) with f(0) = 3, f(1) = 6, f(2) = 12. What type of function is this?
- Exponential (Correct answer)
- Linear
- Quadratic
- Constant
Correct answer: Exponential
Each x-increase of 1 doubles y (×2), indicating exponential growth f(x) = 3 · 2^x.
NBT NBT Mathematics: Functions and Graphs 3
The line y = mx + c has gradient −3 and passes through (1, 2).
What is the equation?