Question

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

Answer 1

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

Answer 2

i don't really understand

Answer 3

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

Answer 4

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