8th Grade Understanding Functions Worksheet (PDF)

8th Grade math worksheet: Understanding Functions – Maths PDF

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This grade 8 functions worksheet for 8th Grade covers understanding functions (Common Core 8.F.A.1, 8.F.A.2, 8.F.A.3), with a free PDF to print.

These 21 problems practice functions, function notation, linear and nonlinear functions and comparing functions (Common Core 8.F.A.1, 8.F.A.2 and 8.F.A.3). Each problem has its own space for work, so print the page and write directly on it.

The problems start with direct skill checks and grow harder as you go. Later items compare functions in different forms and use function rules in real situations. Use the answer key afterwards to check every step.

Grade 8 · Common Core State Standards: 8.F.A.1, 8.F.A.2, 8.F.A.3

Grade 8 functions worksheet: exercises 1 to 10

Exercise 1 – Table function

Does the table represent a function? Explain.

Exercise 2 – Repeated input

Is the relation $(1, 2), (1, 3), (2, 5)$ a function? Explain.

Exercise 3 – Evaluate

If $f(x) = 3x – 2$, find $f(4)$.

Exercise 4 – Evaluate with a square

If $f(x) = x^{2} + 1$, find $f(-2)$.

Exercise 5 – Mapping diagram

Arrows from inputs to outputs.

Does the mapping diagram show a function? Explain.

Exercise 6 – Find the rule

Write a rule $y = mx + b$ for the table.

Exercise 7 – Graph a function

Make a table for $y = x + 2$ with $x = 0, 1, 2, 3$, then graph it.

Exercise 8 – Compare two functions

Function A is $y = 3x + 1$. Function B has the points $(0, 2)$, $(1, 5)$, $(2, 8)$. Compare the rates of change and the initial values.

Exercise 9 – Graph versus equation

Function B is graphed.

Function A is $f(x) = 2x + 5$. Function B is graphed. Which has the greater rate of change?

Exercise 10 – Linear or nonlinear table

Is the function linear or nonlinear? Explain.

Exercises 11 and up

Exercise 11 – Linear equation

Is $y = 5 – 2x$ linear? Give its rate of change and initial value.

Exercise 12 – Which are linear

Which equations are linear? (a) $y = 2x + 3$ (b) $y = x^{2}$ (c) $y = \frac{1}{x}$ (d) $y = -4x$

Exercise 13 – Domain and range

List the inputs and outputs of the function with ordered pairs (1, 3), (2, 5), (3, 7).

Exercise 14 – Solve for the input

If $f(x) = 4x – 3$ and $f(x) = 17$, find $x$.

Exercise 15 – Taxi fare function

Fare rule for 6 miles.

A taxi fare in dollars is $f(x) = 2.5x + 3$, where $x$ is the number of miles. Find the fare for 6 miles and explain what 2.5 and 3 mean.

Exercise 16 – Is it a function?

A relation pairs each student with their favorite color. Is it a function from student to color? Is it a function from color to student? Explain.

Exercise 17 – Area of a square

Area A = s².

The area of a square tile is $A(s) = s^{2}$. Find $A(5)$. Is the function linear? Explain.

Exercise 18 – Phone plans

Plan A and plan B costs.

Plan A costs \$10 to start and \$5 per month. Plan B is $y = 7x$. Which plan costs less after 4 months? After 6 months?

Exercise 19 – Candle

A candle is 12 inches tall and burns down 1.5 inches each hour. Write a function for its height $h$ after $t$ hours. Is it linear? When is it 6 inches tall?

Exercise 20 – Decreasing table

Is $g$ linear? Find its rate of change and write a rule.

Exercise 21 – Explain the vertical line

Explain why the graph of a vertical line, such as $x = 3$, is not a function.

Key facts behind this grade 8 functions worksheet

Key facts

Every input has exactly one output in a function.
Function notation: $f(x) = 2x + 1$ means $f(3) = 7$.
Vertical line test: a graph is a function only if no vertical line touches it twice.
Linear functions have a constant rate of change and graph as straight lines.
Compare functions using rate of change and initial value, whatever their representation.

How to use this grade 8 functions worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the grade 8 functions worksheet as a PDF with the button below and keep it with your notes.

All Grade 8 chapters: Grade 8 math.

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