OpenStudy (anonymous):

Please help!!! Determine algebraically whether the function is even, odd, or neither even nor odd. f(x) = -9 x^(3) + 8x

4 years ago
OpenStudy (mertsj):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (mertsj):

yes

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (jim_thompson5910):

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

4 years ago
OpenStudy (jim_thompson5910):

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

4 years ago
OpenStudy (jim_thompson5910):

which makes f(x) an odd function

4 years ago
OpenStudy (jim_thompson5910):

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

4 years ago
OpenStudy (anonymous):

oh that makes more sense! Thank you!

4 years ago
OpenStudy (jim_thompson5910):

yw

4 years ago