Give an example of an odd function and explain algebraically why it is odd

Question

anonymous · Answer

$$f(x)=x ^{3}$$
by definition, function is odd if f(-x)=-f(x)
so check for the function i geave you as example:
$$f(-x)=-x ^{3}=-f(x)$$

anonymous · Answer

i don't really understand

anonymous · Answer

|dw:1341346480409:dw|
like you can see it's symetric respect to origin. This another "symptom" of odd function

ash2326 · Answer

A function f(x) is said  to be odd if
$$f(-x)=-f(x)$$
or
$$f(x)+f(-x)=0$$
suppose we have $f(x)=x^3$ and so $f(-x)=(-x)^3=-x^3$
now let' see what's $f(x)+f(-x)$
$$f(x)+f(-x)=x^3+(-x^3)=0$$
Hence f(x)= x^3 is an odd function

anonymous · Answer

|dw:1341346598504:dw|