Introduction to Functions Worksheets for 8th Grade
Understand the definition of a function and function notation.
About Introduction to 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.
Functions are the central object of study in all of algebra and beyond. Every equation, graph, and relationship in high school and college mathematics is expressed as a function. Building a clear conceptual understanding here pays dividends throughout a student's entire math education.
What Your Child Will Learn
- Define a function as a relation where each input has exactly one output
- Use function notation f(x) to evaluate and describe functions
- Identify the domain and range of a function from a table or list
- Distinguish between relations that are functions and those that are not
- Represent a function using multiple forms: table, graph, equation, and verbal rule
Worksheets by Difficulty
Start with Easy worksheets to build confidence, then progress to Medium and Hard as your student masters each level.
Understanding the Difficulty Levels
Worksheets 1-3 are Easy level — designed to build confidence with simpler numbers and straightforward problem types. Great for introducing the concept or reviewing basics.
Worksheets 4-7 are Medium level — offering a moderate challenge with larger numbers, varied question types, and more problems per worksheet.
Worksheets 8-10 are Hard level — featuring the most challenging problems including multi-step questions, missing values, and real-world applications.
Tips for Parents & Teachers
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.
Practice finding slope from two points on a graph or table — this skill is tested constantly in middle and high school.
Help your student interpret slope with units: "3 miles per hour" means the slope is 3, with miles per hour as the unit.
The vertical line test is a quick classroom tool, but understanding why it works (one output per input) is more important.
Frequently Asked Questions
What will my child learn from introduction to functions worksheets?
These 8th Grade introduction to functions worksheets help students practice functions, domain, range. Each worksheet provides structured practice with clear instructions and varied problem types.
How often should my 8th Grade student practice introduction to functions?
Consistent practice works best. We recommend 10-15 minutes of focused practice 3-4 times per week. Start with Easy worksheets and progress to Medium and Hard as your student builds confidence.
Are these introduction to functions worksheets free to print?
Yes, all 8th Grade introduction to functions worksheets on K12Worksheets are completely free. You can download and print as many as you need for home or classroom use — no signup required. Each worksheet includes a printable answer key on a separate page.
How do I know which introduction to functions worksheet to start with?
Begin with the Easy worksheets (Worksheets 1–3) to assess your student's current skill level. If they complete these confidently, move to Medium (Worksheets 4–7). Reserve Hard worksheets (Worksheets 8–10) for students who have mastered the basics. If your student struggles with Easy worksheets, revisit prerequisite topics first.