# Can #y=6# be considered a function of #x#?

##### 1 Answer

Yes it can.

#### Explanation:

A **function** is a mapping from one set (of numbers) to another. As long as each input gets mapped to only one output (e.g. the mapping doesn't take the input "3" and map it to both "9" and "27"), the mapping can be considered a function.

A function is like a computer program. It's been programmed to do the same thing to every input it gets. We give it an input, the function takes that input, does something to it, and returns an output. If we give it that same input again, we should get the same output again.

For example, a function

On the other hand, if we had a mapping like *both #+2# and #-2#*. This is

*not*a function, because for every (positive) input, we get

*two*outputs. A function requires "give one thing, get one thing".

Let's say we now have a mapping that takes whatever input we give it, and maps it to "6"—written as *disregards it*, and just returns "6". If we give it "3" again, we're still guaranteed to get "6" and only "6".

## Bonus:

When you graph a mapping, the easiest way to tell if it's a function is to do the "vertical line test". If there's ever a vertical line that passes through the graph more than once, the mapping is *not* a function. Otherwise, it is. The graph of

graph{0x+6 [-11.25, 11.245, -1.99, 9.26]}

Whereas

graph{x=y^2 [-7.55, 14.945, -5.5, 5.75]}