Question

How do you determine if `f(x) = x - absx` is an even or odd function?

Answer 1

An even function is a function where `f(-x)=f(x)` and an odd function is a function where `f(-x)=-f(x)`

Explanation:

Take a look at this `cos` graph:
graph{cos(x) [-10, 10, -5, 5]}
As you can see, the `y`-value for `pi/2` is the same as the `y`-value for `-pi/2`, so it's an even function.

Now look at this `sin` graph:
graph{sin(x) [-10, 10, -5, 5]}

The `y`-value for `pi/2` is `1` whilst the `y`-value for `-pi/2` is `-1`, so it's an odd function.