# How to Evaluate a Function (Mathematics Lesson)

# What Does it Mean to Evaluate a Function?

To evaluate a function means to find the output of a function for a given input.# How to Evaluate a Function

To evaluate a function, substitute the value of the input for the variable in the function.**Question:**Evaluate the function below when

**x = 2**:

**Step 1:**Substitute

**2**for

**x**in the function.

**Step 2:**Use the order of operations to evaluate the expression.

The function evaluated at

**x = 2**is 5.

# How to Evaluate a Function Using a 'Number Machine'

Functions can be visualized as a 'number machine', where a number is put in one end, and another number comes out the other.The function

**f(x) = 2x + 1**is represented by the number machine below:

To evaluate the function at

**x = 2**, insert

**2**into the number machine:

The function evaluated at

**x = 2**is 5.

# How to Evaluate a Function Using Graphical Methods

Functions can be plotted on graphs, with the input**x**on the x-axis and the output

**f(x)**on the y-axis.

Take the function above,

**f(x) = x + 1**, as an example. When this function is plotted, it is a line:

**Question:**Evaluate the function

**f(x) = 2x + 1**when

**x = 2**.

**Step 1:**Find the input

**x = 2**on the x-axis. Draw a line (mentally or otherwise) straight up to the function from the x-axis.

**Step 1:**Draw a line (mentally or otherwise) straight across from the point of the function just found to the y-axis.

The function evaluated at

**x = 2**is 5.

# A Real Example of How to Evaluate a Function

The slider below shows a real life example of evaluating a function.##### Interactive Test

**show**

##### Note

**WHAT IS A FUNCTION?**

A function is a relation between an input and an output.

The input is often denoted

**x**and the function

**f(x)**.

Consider the function below:

- Let the input be denoted by the variable
**x**. - The relation the input plus one:
**x + 1**. - The output is the result of adding one to the input.

# A FUNCTION AS A NUMBER MACHINE

It can be helpful to visualize a function as a machine that takes an input and processes it into an output.Consider the function

**f(x) = x + 1**:

To evaluate the function at a certain value of the input, for example

**x = 1**, put

**1**into the number machine: