Question

How do you know if `f(x)= 2x` is an even or odd function?

Answer 1

Odd.

Explanation:

By definition, for an odd function, `f(-x)=-f(x)` and
for an even function, `f(-x)=f(x)`.

Since for `f(x)=2x` we have that `f(-x)=2(-x)=-2x=-f(x)`.

Therefore this is an odd function.

This is also clear from the graph of the function.

graph{2x [-10, 10, -5, 5]}