Slope as a rate of change
Slope compares the change in output to the change in input. For two points on a nonvertical line, m = (y₂ − y₁)/(x₂ − x₁). A linear relationship has a constant slope.
8th Grade Functions Worksheets
Understand what a function is, identify functions, and evaluate them.
About Functions
Functions are the central concept of all of algebra and the bridge between arithmetic and higher mathematics. Students learn what a function is, how to identify functions from tables, graphs, and mappings, how to distinguish linear from non-linear functions, and how to graph linear functions and interpret slope as a rate of change. This unit rewires how students think about mathematical relationships.
Why Functions Matters for 8th Grade
For 8th Grade students, understanding functions is the most important conceptual advance of the year. The function concept — that each input produces exactly one output — organizes mathematics at every level from algebra through calculus. Slope as a rate of change is arguably the single most applied mathematical concept in all of science and economics.
Learn these skills step by step
Use a worked explanation before choosing a printable set.
Check three selected skills for this grade and use the explained answers to choose your next practice.
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Students first build the concept of a function through multiple representations (tables, graphs, mappings, equations), then distinguish function types, and finally focus deeply on linear functions — graphing them, analyzing slope, and interpreting rate of change in real contexts.
1
Introduction to Functions
Understand the definition of a function and function notation.
10 worksheets · 3 difficulty levels2Identifying Functions
Determine whether a relation is a function using tables, graphs, and mappings.
10 worksheets · 3 difficulty levels3Linear vs. Non-Linear Functions
Compare linear and non-linear functions using tables and graphs.
10 worksheets · 3 difficulty levels4Graphing Linear Functions
Graph linear functions from equations and tables of values.
10 worksheets · 3 difficulty levels5Slope & Rate of Change
Calculate and interpret slope as a rate of change.
10 worksheets · 3 difficulty levelsTips for Parents & Teachers
1
Use everyday function examples: a vending machine is a function (press A3, get chips). A broken vending machine that gives random items is not a function.
2
Practice finding slope from two points on a graph or table — this skill is tested constantly in middle and high school.
3
Help your student interpret slope with units: "3 miles per hour" means the slope is 3, with miles per hour as the unit.
4
The vertical line test is a quick classroom tool, but understanding why it works (one output per input) is more important.
5
Connect linear functions to the proportional relationships from Grade 6 and 7 — they are the same concept with added intercept.
Frequently Asked Questions
What skills does functions cover in 8th Grade?
8th Grade functions builds foundational skills that students need to progress in math. The worksheets on this page cover the available skills listed below, organized from basic to more advanced.
How many functions worksheets are available?
Available subtopics have 10 numbered sets for 8th Grade functions, organized by difficulty level (Easy, Medium, Hard). Each worksheet targets specific skills within this topic area.
What should my student learn before starting 8th Grade functions?
Check the prerequisite topics listed on this page. We recommend students have a solid understanding of those foundational skills before moving on to functions.
How do I know if my 8th Grade student is ready for the Hard functions worksheets?
Start with the Easy worksheets (Worksheets 1–3). If your student completes them confidently with minimal errors, move to Medium (Worksheets 4–7). Reserve the Hard worksheets (Worksheets 8–10) for students who have demonstrated solid mastery at the Medium level. It is perfectly fine to spend more time at a lower difficulty — mastery at each level is more valuable than rushing ahead.
Are these 8th Grade functions worksheets free?
Yes, every functions worksheet on K12Worksheets is completely free to download and print. There is no signup required, no subscription, and no limit on how many you can print. Each worksheet includes a printable answer key on a separate page so parents and teachers can check work quickly.