Question

How do you determine if `abs (x)/ x` is an even or odd function?

Answer 1

we know
`|x|=-x` when `x<0`
and`|x|=x` when `x>0`
so for `f(x)=|x|/x`
putting `x=-x`

`f(-x)=|-x|/-x=-|x|/x=-f(x)`

so it is an odd function

Answer 2

x = 0 is a point of graph-breaking-discontinuity. For x > o, y = `|x|/x = x/x = 1` and for x < 0, y = `-x/x=-1`. Sans x= 0, y is an odd function.

Explanation:

Answer is brief but self-explanatory.