Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for a functions test PDF? Then this Grade 8 test on Understanding Functions and Their Graphs checks the whole chapter, with points for each question. This test has 8 questions worth 20 points in total and should take about 45 minutes. Show how you decide each answer, and use complete sentences where the question asks you to explain.
Standards: 8.F.A.1, 8.F.A.2, 8.F.A.3 · Level: Grade 8
Question 1 Function or not? (2 points)
Decide whether each is a function and explain. (1 point each)
- {(2, 5), (4, 9), (6, 13), (6, 15)}
- {(−1, 4), (0, 4), (1, 4), (2, 4)}
Question 2 Evaluate (2 points)
Let f(x) = 3x² − 5. Find f(−2) and f(4). (1 point each)
Question 3 Which graph? (3 points)
Two graphs are shown.
- Which graph represents a function? (1 point)
- Use the vertical line test to explain. (1 point)
- Name two points on the other graph that share an x-coordinate. (1 point)
Question 4 Compare two functions (3 points)
Function 1: y = 4x + 3. Function 2 is shown in the table.
| x | 0 | 1 | 2 |
|---|---|---|---|
| y | 6 | 8 | 10 |
- Find the rate of change of each. (1 point)
- Find the initial value of each. (1 point)
- Which has the greater output when x = 10? (1 point)
Question 5 Linear or not? (3 points)
Look at the table.
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | 3 | 7 | 13 | 21 |
- Find the change in y for each step of 1 in x. (1 point)
- Is the function linear? Explain. (1 point)
- Write a rule for the linear function with (0, 5), (1, 8), (2, 11). (1 point)
Question 6 Graph and equation (3 points)
The graph shows a function. A second function is y = 2.5x + 1.
- Find the rate of change and initial value of the graph. (1 point)
- Which function changes faster? (1 point)
- Write the equation of the graphed function. (1 point)
Question 7 Rising water (2 points)
The depth of a fish tank is d(t) = 5t + 8 inches after t hours. Find d(4) (1 point) and the time when the depth is 43 inches (1 point).
Question 8 Is area linear? (2 points)
The area of a square is A = s². Use the sides 1, 2 and 3 to show that the function is not linear.
