A mathematical function is like a special rule that takes each number from one group and gives back exactly one number from another group.

We call the first group the "domain" and the second group the "range."

To break it down simply:

• If we say $f$ is a function,
• For every number $x$ in the domain,
• There is one and only one number $y$ in the range, which we can write as $y = f(x)$.

Example:

• Think about the function $f(x) = x^2$.
• This means when we put in a number $x$, we will always get one result $y$.

Graphing It: We can use a graph to see this more clearly.

For the function $f(x)$, the graph looks like a U-shaped curve called a parabola.

This graph shows how each $x$ value links to one $y$ value.