For f(x) = 2x + 3, find f(4).
- Replace x with 4: f(4) = 2(4) + 3.
- Multiply, then add: 8 + 3.
Answer: 11
Function Notation Worksheets
Evaluate a function at a given input, showing substitution before calculation.
Learn the skill
Function notation: what f(x) means
f(x) means the output of a function f when its input is x. The parentheses identify an input; they do not mean f multiplied by x. To evaluate a formula, replace every occurrence of the input variable.
A method you can use
- Identify the input inside the parentheses.
- Substitute that input everywhere the variable occurs, using parentheses for negative numbers or expressions.
- Calculate in order and check any domain restrictions, such as a denominator that cannot be zero.
Worked examples
For g(x) = x² − 1, find g(−3).
- Use parentheses: (−3)² − 1.
- The square is 9; subtract 1.
Answer: 8
For h(x) = 3x − 2, find h(a + 1).
- Replace x with the whole expression: 3(a + 1) − 2.
- Distribute and simplify: 3a + 3 − 2.
Answer: 3a + 1
Try it yourself
Solve these before opening the answers. The printable sets below give you more practice.
1. For f(x) = 5x − 2, find f(3).
Show answer and explanation
13
5(3) − 2 = 15 − 2 = 13.
2. For g(x) = x² + 2, find g(−4).
Show answer and explanation
18
(−4)² + 2 = 16 + 2.
Before you begin
Evaluate expressions and work with signed numbers.
Choose your level
- Easy: Substitute positive inputs into linear functions.
- Medium: Use negative inputs and coefficients in linear functions.
- Hard: Evaluate quadratic expressions at positive or negative inputs.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
If f(x) = 3x - 3, find f(6).
2
If f(x) = 7x - 9, find f(4).
3
If f(x) = 8x + 1, find f(1).
4
If f(x) = 7x - 5, find f(5).
5
If f(x) = 6x + 7, find f(3).
6
If f(x) = 9x + 8, find f(4).
Answer Key
1. 152. 193. 94. 305. 256. 44