Question

How do you determine if `y= 5^(3 + 2x)` is an even or odd function?

Answer 1

This function is not even and is not odd.

Explanation:

by definition, an even function is a function that does not change if instead of `x` we use `-x`. An odd function changes the sign when `x` is swapped with `-x`.

Then let's try

`y=5^(3+2x)`

and we substitute
`x->-x`

`y=5^(3-2x)`

The two functions are clearly different.
For example, when `x=1` we have

`y=5^(3+2)=5^5`

and for `x=-1`

`y=5^(3-2)=5^1=5`.

The function does not stay unchanged neither it swaps the sign.
The function is not even and is not odd.