Function notation and definitions work together to clearly describe math relationships.

A function is a special type of relationship where every input (often called the independent variable, $x$) goes to exactly one output (known as the dependent variable, $y$). This is really important! For example, to be a function, a set of values must pass something called the vertical line test.

Function Notation

Function notation is usually written as $f(x)$, which is a simple way to show we are working with a function. Here’s an example:

• If $f(x) = 2x + 3$, when we plug in $x = 4$, we get: $f(4) = 2(4) + 3 = 11$

Importance of Definitions

Having a clear definition helps prevent confusion when we do math. About 30% of 9th graders find these ideas tricky at first.

By having clear definitions and using function notation, students can really improve their understanding. This leads to better skills in algebra, where functions are very important for learning advanced topics later on.