1. Can the X values repeat in a function?
2. Can a function have repeat outputs?
3. What makes a function not a function?
4. How do you tell if a function is a function?

Can the X values repeat in a function?

A function is a relation in which the members of the domain (x-values) DO NOT repeat. So, for every x-value there is only one y-value that corresponds to it.

Can a function have repeat outputs?

A function is a relation between sets where for each input, there is exactly one output. So functions cannot have the same output.

What makes a function not a function?

If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output. A function has only one output value for each input value.

How do you tell if a function is a function?

Determining whether a relation is a function on a graph is relatively easy by using the vertical line test. If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function.