Resources/Introduction to functions
Grade 8•Printable worksheet + answer key•CC0 license

Introduction to functions

Understand function notation, tables, graphs, and linear vs nonlinear

Students learn how functions map inputs to outputs, read tables and graphs, and recognize linear patterns.

Print-ready worksheet with answer key and quick teaching tips.

Grade 80 problems10 minAnswer key included
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Ready-to-teach

Clear steps, examples, and practice in one printable page.

Misconception-proof

Highlights common mistakes and how to fix them quickly.

Open license

CC0: free to copy, adapt, and share without attribution.

Quick overview

This free functions worksheet for grade 8 builds confidence with function notation, tables, graphs, and linear vs nonlinear relationships.

Lesson plan snapshot

15-20 min
  • Warm-up (3 min): review ordered pairs and input/output language.
  • Model (5 min): solve the worked example together.
  • Guided practice (5 min): complete problems 1-3 as a group.
  • Independent practice (7 min): finish the remaining problems.

Materials: graph paper, pencil

Learning targets

  • Understand that a function assigns exactly one output to each input.
  • Use function notation f(x) to evaluate outputs.
  • Identify functions from tables and graphs.
  • Distinguish linear from nonlinear functions.

Step-by-step approach

  1. 1Check that each input has exactly one output.
  2. 2Read tables from input to output and use ordered pairs on graphs.
  3. 3Evaluate f(x) by substituting the input value.
  4. 4Look for constant rate of change to identify linear functions.
  5. 5Describe whether outputs increase or decrease as inputs grow.

Common mistakes

Mistake

Thinking f(x) means f times x

Try instead

f(x) is notation meaning "the output when input is x"

Mistake

Confusing linear with any straight pattern

Try instead

Linear means y = mx + b form

Worked example

Guided
Is y = x^2 a function? Is it linear?
  1. Each input x gives exactly one output x^2, so it is a function.
  2. The equation has x^2, so the rate of change is not constant.
  3. Therefore it is nonlinear.
Answer: Yes, it is a function; no, it is not linear.

Related resources

Linear equations

Slope, slope-intercept form, and graphing lines.

View resource

Coordinate plane

Plot points and read ordered pairs.

View resource

Practice problems

0 problems • 10 min

Printable worksheet

    Answer key

    0 answers

      Teacher tips

      • TUse mapping diagrams before moving to tables and graphs.
      • THave students check repeated x-values when testing for functions.
      • TConnect linear functions to constant rate of change stories.

      Parent tips

      • PAsk your child to explain what f(3) means in words.
      • PUse everyday examples like input hours to output total cost.
      • PPractice spotting whether tables change by a constant amount.

      Open license

      You are free to copy, adapt, and share these materials. No attribution required. Released under Creative Commons CC0 1.0 (public domain).