Function Worksheets
reviewed by Jo-ann Caballes
Updated on October 16, 2026
A function is a rule that gives exactly one output for every input. If the rule is “add 3,” an input of 5 always gives 8. Our free function worksheets for grades 5–9 start with simple input-output tables and build up to function notation, where students evaluate f(x) and decide whether a function is linear.
Free Function Worksheets with Answers (PDF)
The worksheets are arranged from easiest to hardest. The function table worksheets (grades 5–6) ask students to fill in In and Out boxes using rules like “subtract 3,” “add 4.42,” or “divide by 6,” and to find the rule from a finished table. The function worksheets (grades 8–9) move on to f(x) notation: evaluating functions, finding a linear function from a table, writing area and volume functions, and telling linear from non-linear functions. Every PDF includes an answer key.
How Functions Work
Function tables: input and output
A function table lists inputs in one column and outputs in the other. To complete it, apply the rule to each input. With the rule “multiply by 2,” the inputs 3, 5, and 8 give the outputs 6, 10, and 16. To find a missing rule, compare the pairs: if 14 → 28 and 17 → 34, the rule is “multiply by 2.”
Function notation: f(x)
In middle school, the rule is written as an equation. In f(x) = 3x − 2, x is the input and f(x) is the output. To evaluate the function, substitute the input: f(4) = 3(4) − 2 = 10.
Linear and non-linear functions
A function is linear when the output changes by the same amount every time the input increases by 1. In the table x = 1, 2, 3 and y = 2, 4, 6, the output grows by 2 each time, so the function is linear: f(x) = 2x. If the changes are not equal, the function is non-linear.
Benefits of Function Worksheets
Build the idea of a rule
Function tables help younger students see that a rule turns every input into an output. This prepares them for patterns, equations, and algebra.
Connect tables, equations, and words
Students practice moving between a table, a written rule, and an equation like f(x) = 5x + 5. Seeing the same function in different forms makes the concept easier to understand.
Prepare for Algebra 1
Evaluating functions, writing functions from real situations, and identifying linear functions are core skills in 8th grade and Algebra 1. They also lead directly to graphing lines and working with slope.
More function worksheets
- Domain and range worksheets
- Slope worksheets
- Composite functions worksheet
- Quadratic functions worksheet
- Algebra 1 worksheets
Frequently Asked Questions
What is a function in math?
A function is a rule that assigns exactly one output to each input. For example, the rule “add 3” turns 2 into 5 and 10 into 13. Functions can be shown as tables, equations, graphs, or words.
How do you complete a function table?
Apply the rule to each input to get the output. If the rule is missing, look at the pairs you already have and find the operation that turns every input into its output, then use it to fill in the empty boxes.
How do you evaluate f(x)?
Replace x with the given number and simplify. For f(x) = 7x + 4, f(2) = 7(2) + 4 = 18.
What grade are these function worksheets for?
They cover grades 5–9. Function tables with whole numbers and decimals fit grades 5–6. Function notation, evaluating f(x), and linear functions are taught in grade 8 and Algebra 1.
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