Determine algebraically whether the functions are odd, even, or neither

Switch all x variables to - x.

If the new equation is the same as before (y = x^2 + |x|) then the equation is even.

If the new equation is the exact opposite (y = x^3 - - > y = - x^3) then the equation is odd.

If the equation turns out to be neither (y = x+1) then the answer is neither.

It can never be both.

Try graphing it out too! Even ones are symmetrical across the y axis. Odd ones can be rotated 180 degrees and still create the same line.