Every function has two key sets of values: its Domain and its Range. Let's make this simple.

The Domain is the set of all possible *input* values. These are the 'x' values.

The Range is the set of all possible *output* values. These are the 'y' values that come out of the function.

Think of a function as a bread-making machine.

The Domain is all the ingredients you are *allowed* to put into the machine (flour, water, yeast).

The Range is all the possible things that can come out of the machine (a loaf of bread).

For most simple linear and polynomial functions, the domain is 'all real numbers.' You can plug in any x you want.

You only have to worry about the domain when you have two specific situations: division and square roots.

You cannot divide by zero, so any x-value that makes the denominator zero is NOT in the domain.

You cannot take the square root of a negative number, so any x-value that makes the inside of a square root negative is NOT in the domain.