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# Evaluating a Function

(KS4, Year 10)

## The Lesson

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**.

## A Note on Notation

If a function**f**is evaluated at a number (e.g.

**2**), this is denoted

**f(2)**.

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