Many things in math are 'relations,' but only the special ones get to be called 'functions.' Here's how to tell the difference.

A Relation is any set of ordered pairs (x,y). It's any relationship between two variables at all.

A Function is a special, well-behaved relation where every input (x) has exactly one output (y).

The Key Question: Can any 'x' value lead to more than one 'y' value?

If you have a set of points, like {(2,3), (3,4), (2,5)}, it is NOT a function. Why? Because the input '2' has two different outputs (3 and 5).

If you have a graph, there is a simple, visual test: The Vertical Line Test.

Take a vertical line (like a pencil) and sweep it across your graph from left to right.

If at any point your vertical line touches the graph in more than one spot, it is NOT a function.

This test works because a vertical line represents a single x-value. If it hits the graph twice, that x-value has two y-values.

A function must be reliable. It must be predictable. For every one input, you get one and only one output. That's the law.