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.

Lesson Slides

The slider below another example of how to evaluate functions. Open the slider in a new tab

A Note on Notation

If a function f is evaluated at a number (e.g. 2), this is denoted f(2).
Help Us To Improve Mathematics Monster

  • Do you disagree with something on this page?
  • Did you spot a typo?
Please tell us using this form

See Also

What is the order of operations?