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.
Answer:
neither
Step-by-step explanation:
To check if the function is odd, try replacing x by −x :
[tex]y = x^2 - 2x - 8[/tex] → Original equation
[tex]y = (-x)^2 - 2(-x) -8[/tex]
[tex]y = (-1)^2 (x)^2 +2x - 8[/tex] → as you can tell the equation has already changed
[tex]y = -x^2 + 2x - 8[/tex] → 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:
In this case, you can tell there is an odd and an even which makes this function neither
Hope this helps!
