A function is a rule that assigns a unique output value to each input value.

We often denote functions by \(f(x)\), where \(x\) is the input variable.

You can think of functions as machines: you insert an input value, the machine follows a rule, and spits out the output value.

For example, \(f(x) = x^2 + 2\) is a function because each input value, \(x\) has a unique output value, \(x^2 + 2\). Let's look at a few function values:

• \(f(2) = 2^2 + 2 = 6\)
• \(f(-1) = (-1)^2 + 2 = 3\)
• \(f(0)= (0)^2 + 2 = 2\)