Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Begin with simple tests of the one-output rule, then move to rates of change, initial values and modeling.
Standards: 8.F.A.1, 8.F.A.2, 8.F.A.3 · Level: Grade 8
Problem 1 Ordered pairs ★★★
Decide whether each set of ordered pairs is a function: (a) {(1, 4), (2, 7), (3, 10), (4, 13)} (b) {(2, 5), (2, 8), (3, 9)}
Problem 2 Mapping diagram ★★★
Is the relation in the mapping diagram a function? If so, describe the rule.
Problem 3 Table rule ★★★
The table shows a function. Find its rule.
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y | 6 | 9 | 12 | 15 |
Problem 4 Function notation ★★★
Let f(x) = 4x − 7. Find f(5), f(−2) and f(0).
Problem 5 Vertical line test ★★★
Slide an imaginary vertical line across this graph. Does the graph define a function?
Problem 6 Input and output ★★★
A function has the rule y = 2x + 9. Find the outputs for the inputs 3, 6 and 10.
Problem 7 Quadratic table ★★★
Let g(x) = x² − 3. Complete a table for x = −2, −1, 0, 2, 4. Does the output ever repeat?
Problem 8 Linear or nonlinear tables ★★★
Decide whether each table is linear.
Table 1
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | 5 | 9 | 13 | 17 |
Table 2
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | 2 | 5 | 10 | 17 |
Problem 9 Side and area ★★★
A graph plots the area of a square against its side length. Calculate the change in area per unit of side from side 1 to side 3, then from side 2 to side 3. The plotted points are (1, 1), (2, 4) and (3, 9). Does a straight line fit these points?
Problem 10 Compare two functions ★★★
Function A: y = 2.5x + 4. Function B is shown in the table. Which has the greater rate of change, and which has the greater initial value?
| x | 0 | 2 | 4 |
|---|---|---|---|
| y | 3 | 9 | 15 |
Problem 11 Graph versus equation ★★★
The graph shows Function C. Function D is y = 3x − 1. Compare their rates of change and their y-intercepts.
Problem 12 Spot the linear equations ★★★
Which equations are linear? (a) y = 7x − 2 (b) y = x² (c) y = 4 − x/2
Problem 13 Find the rule ★★★
Write a rule for the function.
| x | 2 | 4 | 6 | 8 |
|---|---|---|---|---|
| y | 7 | 13 | 19 | 25 |
Problem 14 Repeated outputs ★★★
Is {(Ava, June), (Ben, June), (Cy, August)} a function from names to birth months? Is the reverse pairing {(June, Ava), (June, Ben), (August, Cy)} a function?
Problem 15 Pool water level ★★★
A wading pool holds 12 inches of water and a hose raises the depth by 4 inches per hour. Write the depth function d(t), find d(6.5), and find when the depth is 60 inches.
Problem 16 Two phone plans ★★★
Plan A: cost C = 0.10m + 15 for m minutes. Plan B: cost $28 for 100 minutes, $38 for 200 minutes and $48 for 300 minutes. Compare the rates and the initial fees. Which plan costs less?
Problem 17 Perimeter and area ★★★
Make a table of P = 4s and A = s² for sides 1 through 5. Decide which one is linear and find the side where the two values coincide.
Problem 18 Constant versus vertical ★★★
Explain why y = 5 is a function but x = 5 is not.
Problem 19 Points on a line ★★★
A function contains the points (1, 6), (3, 14) and (6, 26). Show that it is linear, write its rule and find f(10).
Problem 20 Fence and seed ★★★
A square garden has side s feet. The fence cost is C = 12s dollars, because it is priced per foot of side length. Seed costs $0.50 per square foot: the cost is S = 0.5s². Find both costs for s = 6, find the side length where they match, and decide which cost is larger at s = 30.
