Question

Please help!!!
Determine algebraically whether the function is even, odd, or neither even nor odd.

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

Answer 1

If the f(x) = f(-x) the function is even
If the f(x)=-f(-x) the function is odd.

Answer 2

so is f(-x)=9x^(3)-8x
and -f(-x)=9(-x)^(3)-8(-x)
???

Answer 3

yes

Answer 4

so does -f(-x) come out to be -9x^(3)+8?

Answer 5

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


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


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


f(-x) = 9x^3 - 8x


-------------------------------------------------------

f(-x) = 9x^3 - 8x


-f(-x) = -(9x^3 - 8x)


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

Answer 6

So we can see that f(x) doesn't equal f(-x)

but

f(x) does equal -f(-x)

Answer 7

which makes f(x) an odd function

Answer 8

the shortcut is to notice the exponents on the polynomial

if all the exponents are even, then the polynomial function is even

if all the exponents are odd, then the polynomial function is odd

Answer 9

oh that makes more sense! Thank you!

Answer 10

yw