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

Apr 8, 2018

even.

#### Explanation:

$3 x = | \setminus y |$

substituting $y$ for $- y$

$3 x = | \setminus \pm y |$

$3 x = | \setminus y |$

so it's even.
In general:
A function is even $\rightarrow$ it is symmetrical about the $y$ axis
and an odd function$\rightarrow$ 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 $f \left(x\right) = f \left(- x\right)$
like $y = {x}^{2}$ if You substitute for each $x$ for $- x$ You get
$y = {\left(- x\right)}^{2} = {x}^{2} = f \left(x\right)$ so it's even
and same goes for $y = | \setminus x |$

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

and it will be neither even nor odd if it gives You something else like $y = 3 x + 2$
if You substitute $x$ for $- x$
you get:
$y = - 3 x + 2 \ne \pm f \left(x\right)$