Functions Practice Questions
Common Core (US) · Common Core Math Grade 8 · 146 free MCQs with instant results and detailed explanations.
146
Total
45
Easy
81
Medium
20
Hard
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Sample Questions from Functions
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
Which of the following represents a linear function?
A.
f(x) = 3x + 5
B.
f(x) = x^2 + 2
C.
f(x) = sin(x)
D.
f(x) = 1/x
Show Answer & Explanation
Correct Answer: A
A linear function has a constant rate of change, which is represented by the formula of the form f(x) = mx + b. Here, f(x) = 3x + 5 is in that form with m = 3 and b = 5.
Q2
Easy
If f(x) = 2x + 1, what is f(3)?
A.
7
B.
9
C.
6
D.
5
Show Answer & Explanation
Correct Answer: A
To find f(3), substitute x with 3 in the function f(x) = 2x + 1. So, f(3) = 2(3) + 1 = 6 + 1 = 7.
Q3
Easy
The function g(x) is defined as g(x) = 4x. What is the output when x = -2?
A.
-8
B.
8
C.
2
D.
0
Show Answer & Explanation
Correct Answer: A
To find g(-2), substitute -2 into the function: g(-2) = 4(-2) = -8. Thus, the output is -8.
Q4
Medium
If f(x) = 3x - 2, what is f(4)?
A.
10
B.
12
C.
14
D.
16
Show Answer & Explanation
Correct Answer: A
To find f(4), substitute x with 4 in the function: f(4) = 3(4) - 2 = 12 - 2 = 10.
Q5
Medium
Which graph represents a function?
A.
A straight line
B.
A circle
C.
A parabola
D.
A horizontal line
Show Answer & Explanation
Correct Answer: A
A function must assign exactly one output for every input. A straight line meets this criterion, while a circle fails the vertical line test and does not represent a function.
Q6
Medium
Which of the following is the correct interpretation of the slope in the function f(x) = -4x + 7?
A.
The function decreases by 4 units for each unit increase in x.
B.
The function increases by 4 units for each unit increase in x.
C.
The function has a constant value of 7.
D.
The function has no slope.
Show Answer & Explanation
Correct Answer: A
The slope of -4 indicates that for each 1 unit increase in x, the value of f(x) decreases by 4 units, indicating a negative relationship.
Q7
Medium
If a function is defined as g(x) = x^2 + 1, what is g(-3)?
A.
10
B.
8
C.
6
D.
4
Show Answer & Explanation
Correct Answer: A
To find g(-3), substitute -3 into the function: g(-3) = (-3)^2 + 1 = 9 + 1 = 10.
Q8
Hard
The graph of the function f(x) = ax^2 + bx + c has its vertex at the point (2, -3). If a = 1, what are the values of b and c?
A.
b = -4, c = -1
B.
b = -2, c = 1
C.
b = -8, c = 13
D.
b = -6, c = 6
Show Answer & Explanation
Correct Answer: A
For a parabola in vertex form y = a(x-h)^2 + k, the vertex (h, k) indicates that h = -b/(2a) and k = c - (b^2/(4a)). Here, h = 2, a = 1, hence -b/(2) = 2 implies b = -4. To find c, substitute vertex coordinates into the function: -3 = 1(2)^2 - 4(2) + c, which leads to c = -1.
Q9
Hard
Which of the following represents a linear function?
A.
y = 3x + 5
B.
y = x^2 - 4
C.
y = sin(x)
D.
y = e^x
Show Answer & Explanation
Correct Answer: A
Option A represents a linear function because it is in the form y = mx + b, where m is the slope and b is the y-intercept. The other options involve non-linear equations.
Q10
Hard
If f(x) = x^2 - 2x + 1 represents a function, which of the following statements is true about its graph?
A.
It opens upwards and has a minimum point.
B.
It opens downwards and has a maximum point.
C.
It is a straight line.
D.
It has no real roots.
Show Answer & Explanation
Correct Answer: A
The function f(x) = x^2 - 2x + 1 is a quadratic function that opens upwards (the coefficient of x^2 is positive) and has a minimum point at the vertex, which occurs at x = 1.
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Functions — Common Core (US) Common Core Math Grade 8 Practice Questions Online
This page contains 146 practice MCQs for the chapter Functions in Common Core (US) Common Core Math Grade 8. The questions are organized by difficulty — 45 easy, 81 medium, 20 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.