Question

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

Answer 1

Odd

Explanation:

Call the function

`f(x)=1/x`

Now,

`f(x)` is even if `f(-x)=f(x)`.

`f(x)` is odd if `f(-x)=-f(x)`.

Find `f(-x)`:

`f(-x)=1/(-x)=-1/x`

Since `-1/x=-f(x)`, the function is odd.

graph{1/x [-9.295, 10.705, -4.48, 5.52]}

A special feature of odd functions is that they have "origin symmetry." This means that they can be reflected over the point `(0,0)` and look identical.