Function Table — Definition, Formula & Examples
A function table is a chart that organizes input values and their corresponding output values for a given function rule. Each row (or column) pairs one input with exactly one output.
A function table is a tabular representation of a function in which each entry associates an element from the domain with its unique image in the range, making the mapping explicit for a finite set of domain values.
How It Works
You start with a rule, such as , and a list of input values. Substitute each input into the rule to calculate the output. Record both values side by side in the table. Reading the finished table, you can quickly spot patterns, identify the function rule, or plot points on a coordinate plane.
Worked Example
Problem: Complete the function table for the rule y = 3x − 2 using the inputs x = 0, 1, 2, 3, and 4.
Step 1: Substitute x = 0 into the rule.
Step 2: Substitute x = 1, 2, 3, and 4 the same way.
Step 3: Write all pairs in the table: (0, −2), (1, 1), (2, 4), (3, 7), (4, 10).
Answer: The completed function table has outputs −2, 1, 4, 7, and 10 for inputs 0 through 4.
Why It Matters
Function tables appear constantly in middle-school math and introductory algebra when you first study linear and nonlinear relationships. They also show up in science classes for recording experimental data and identifying how one variable depends on another.
Common Mistakes
Mistake: Applying the rule to the output instead of the input (e.g., plugging a y-value back into the rule as if it were x).
Correction: Always substitute the value from the input column into the rule. The result goes in the output column, not back into the input.