How-to · Updated October 2, 2026
How do you complete a function table?
Direct answer
Substitute each input into the rule. For y = 2x + 1 and x from −2 to 2, the outputs are −3, −1, 1, 3, 5. One line of work is y = 2(−2) + 1 = −3.
y = 2x + 1
| x | −2 | −1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | −3 | −1 | 1 | 3 | 5 |
First differences are all 2 → linear. Rate of change (slope) = 2 ÷ 1 = 2.
y = −5x − 1
| x | −2 | −1 | 0 | 1 |
|---|---|---|---|---|
| y | 9 | 4 | −1 | −6 |
First differences are all −5 → linear. Rate of change (slope) = −5 ÷ 1 = −5.
y = x² − 3
For x from −2 to 2 the outputs are 1, −2, −3, −2, 1. Second differences are all 2 → quadratic (parabola), leading coefficient a = 1, opening up.
Limits
- Follow the order of operations: exponents and multiplication before addition. y = 3 + 2x is the same as y = 2x + 3.
- Some rules are undefined at an input. y = 1/x has no output at x = 0.
- A table lists ordered pairs. It does not by itself prove the rule unless every required input is filled.
Use the calculator
The reverse problem: how to find the function from a table. Fill any rule in the function table calculator.