Question

what is an example of an odd function. Please explain why its odd?

Answer 1

odd functions are the functions have \[f(-x) = -f(x)\]
like polynomials x,x^3,...
and sin(x)
as you can see that
for f(x)=x^3
f(-x)=-f(x)=-x^3

Answer 2

Thanks

Answer 3

So, basically they have odd exponents and you know that when you take the negative of an odd exponent it remains negative.. So putting -x into an odd exponent is a way to "test" if it's odd.

Answer 4

So f(x)=x^3 would be an odd function because the 3 is odd

Answer 5

yes
but odd does not necessarily mean all odd exponents
for example
\[f(x)=\frac{x}{x^2-1}\] is odd

in that example
\[f(3)=\frac{3}{9-1}=\frac{3}{8}\] and \[f(-3)=\frac{-3}{9-1}=-\frac{3}{8}\]

Answer 6

But wouldn't the denominator make it neither?

Answer 7

no
for a polynomial to be odd, all exponents must be odd.
but the example i wrote above is a rational function not a polynomial

the definition of odd is what you said
\(f\) is odd means \(f(-x)=-f(x)\) and in the example i wrote above
\[f(-x)=\frac{-x}{(-x)^2-1}=-\frac{x}{x^2-1}=-f(x)\]

Answer 8

of course there are functions besides polynomial functions. for example sine is odd

Answer 9

Oh... I understand :) thanks

Answer 10

Thanks this help a lot :)