Question

Is the function even, odd or neither? y=x^2-2x-8

Answer 1

Answer:

neither

Step-by-step explanation:

To check if the function is odd, try replacing  x  by  −x :

$y = x^2 - 2x - 8$ → Original equation

$y = (-x)^2 - 2(-x) -8$

$y = (-1)^2 (x)^2 +2x - 8$  → as you can tell the equation has already changed

$y = -x^2 + 2x - 8$  → even if we factor out the negative 1 the 8 at the end would turn positive

Thus,  y  is neither odd nor even.

Another way, if you deal with a polynomial:

Check which of the coefficients are non-zero:

• Before even powers of x only? Even

• Before odd powers of x only? Odd

In this case, you can tell there is an odd and an even which makes this function neither

Hope this helps!

Answer 2

It is neither.

To be even, f(x) must equal f(-x).

If you substitute -x for x, you'd get

     y = (-x)^2 - 2(-x) -8

     y = x^2 +2x -8

This is not the same as the original, so this is not even.

To be odd, f(x) must equal -f(-x).

If you take the -x substitution from the last step and then multiply it by -1, you'd have:

      y = -1 (x^2 +2x -8)

      y = -x^2 -2x +8

This is not the same as the original either.

The function is neither even nor odd.