Question

How do you determine if `y=2x^5+x` is an even or odd function?

Answer 1

`y=2x^5+x` is an odd function

Explanation:

If `y_((-x)) = y_x` then the function is even

If `y_((-x))=-y_x` then the function is odd

Given
`color(white)("XXX")y_x=2x^5+x`

then
`color(white)("XXX")y_((-x)) = 2(-x)^5+(-x)`

`color(white)("XXXXXXX")=-2x^5-x`

`color(white)("XXXXXXX")=-(2x^5+x)`

`color(white)("XXXXXXX")=-y_x`

So the function is odd