Question

How do you determine if `3x = |y|` is an even or odd function?

Answer 1

even.

Explanation:

`3x=|\y|`

substituting `y` for `-y`

`3x=|\+-y|`

`3x=|\y|`

so it's even.
In general:
A function is even `rarr` it is symmetrical about the `y` axis
and an odd function`rarr` if it's symmetrical about the origin

but if You want to know through an equation you just substitute for each `x` for `-x`

A function is even
if `f(x)=f(-x)`
like `y=x^2` if You substitute for each `x` for `-x` You get
`y=(-x)^2=x^2=f(x)` so it's even
and same goes for `y=|\ x|`

And it will be odd if `f(x)=-f(-x)`
ex: `y=x`
if You substitute `x` for `-x`you get
`y=-x=-f(x)`

and it will be neither even nor odd if it gives You something else like `y=3x+2`
if You substitute `x` for `-x`
you get:
`y=-3x+2 !=+-f(x)`