# How to Evaluate a Function

## Evaluating a Function

A function is a relation between a set of inputs and a set of outputs, such that each input is related to exactly one output.

Evaluating a function means putting an input into a function, and finding the output it relates to.

## Understanding Evaluating a Function

To evaluate a function means to see what output an input is mapped to.

The image below shows a mapping diagram which relates a set of inputs to a set of outputs.

If we wanted to evaluate the function when the input is 2, we would see which output it is mapped to. Imagine we have the function below: If we evaluate the function at x = 2, we need to find f(2).

## A Real Example of How to Evaluate a Function

Evaluating a function is easy.

### Question

Evaluate the function f(x) = 2x + 1 at x = 2.

# 1

Write the function.

f(x) = 2x + 1

Note: 2x = 2 × x.

# 2

Substitute x = 2 into the function.

f(2) = 2 × 2 + 1

f(2) = 4 + 1

f(2) = 5

If we evaluate f(x) = 2x + 1 at x = 2, we get 5.

f(2) = 5.

## Slider

The slider below another example of how to evaluate functions.

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