# 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**.

### Step-by-Step:

# 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

### Answer:

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

**f(2) = 5**.