SOLUTION: Which characteristic is correct for the function f(x)=-6x^5+4x^3 ? both even and odd even neither even nor odd odd

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Question 1129484: Which characteristic is correct for the function f(x)=-6x^5+4x^3 ?


both even and odd
even
neither even nor odd
odd
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Which characteristic is correct for the function f(x)=-6x^5+4x^3 ?
First we do it visually.
If it is symmetrical with respect to the y-axis, it is even.
If it is symmetrical with respect to the origin, it is odd.

graph%28400%2C400%2C-1.3%2C1.3%2C-1.3%2C1.3%2C-6x%5E5%2B4x%5E3%29

It's symmetrical with respect to the origin so it's an ODD function.

Next we do it algebraically:

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

f(x) = -6x5+4x3
f(-x) = -6(-x)5+4(-x)3
f(-x) = -6(-x5)+4(-x3)
f(-x) = 6x5-4x3
f(-x) = -(6x5+4x3)
f(-x) = -f(x)

The function is odd.

Edwin