What is a Function Rule? Definition and Examples

A function rule is a rule that shows the relationship between the input and the output of a function.

For example, consider the function f(x) = 3x + 2. What is the function rule?

The input is x and the output is f(x).

The function rule explains how to find the output. To find the output, multiply the input by 3 and then add 2.

Using the function rule, you may end up with the following two sets.

x : {1, 2, 3, 4, 5, 6, 7, ...}

f(x): {5, 8, 11, 14, 17, 20, 23, ...}

The function rule may involve, just to mention a few, addition, subtraction, multiplication, division, exponentiation, or a combination of these.

For example, f(x) = x2 involves exponentiation.

The function rule indicates that you need to square the input.

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