A **function** is a rule that connects** inputs** and **outputs**.

Every input has **one corresponding value** as an output.

**f(x) **means a function of **x**, where **x** is a specific input.

**f(x) = x ^{2} + 3 **means a functions of

**x**where you square

**x**and then add 3 to it.

If you want to work out the output when the input is 3, we write it like this:

**f(3)= 3 ^{2} + 3 = 9 + 3 = 12**

Sometimes the input is an **algebraic term**.

If this is the case, replace each letter **x** with the desired input.

Let's write the function written above** f(x) = x ^{2} + 3** as a function with input

**4x**:

**f(4x) = (4x) ^{2} + 3 = 16x^{2} + 3**

In this activity, we will use formal notation (shown in the examples above) to express and calculate inputs and outputs of functions.