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

1 Answer
Yahia M.
Apr 8, 2018

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)#

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