Question

Is this equation odd, even, or neither?

f(x) = -9 x3 + 8x

Answer 1

Sorry, that's supposed to be Determine algebraically whether the function is even, odd, or neither even nor odd.

f(x) = -9 x^3 + 8x. Whoops.

Answer 2

plug in -x

Answer 3

if f(-x)=f(x) then f is even
if f(-x)=-f(x) then f is odd

Answer 4

\[f(x)=-9x^3+8x \\ f(-x)=-9(-x)^3+8(-x)\]
can you rewrite (-x)^3?

Answer 5

and equation is old when the highest power of the independent variable is old

Answer 6

not necessarily true

Answer 7

what if you had f(x)=-9x^3+1
that would be neither

Answer 8

although they are also some rules guiding it. thanks @freckles

Answer 9

you mean if you have a polynomial
and in that polynomial all the powers are odd then the polynomial function is also odd
in the example f(x)=-9x^3+1
the powers are 3 and 0

Answer 10

this function is neither because you have not all the powers are odd

Answer 11

and if all the powers are even in the polynomial then the polynomial function is even

Answer 12

ok. thanks for the correction

Answer 13

but it said to find out algebraically if the function is odd or even or neither
and that is why we are doing it the long way above

Answer 14

Heh.. I suppose this one was a bit self-explanatory. Thanks.