Question

How do you determine if `y= 1/x` is an even or odd function?

Answer 1

I'd say odd.

Explanation:

You can check by considering general rule:
ODD if: `f(-x)=-f(x)`
EVEN if: `f(-x)=f(x)`

So basically test a positive and a negative `x` such as, for example:
`2 and -2`

You get:
`f(x)=f(2)=1/2=0.5`
`f(-x)=f(-2)=-1/2=-0.5`

so basically we have that:

`f(-x)=-0.5=-f(x)`

giving an ODD function.