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

An odd function could be

f (x) = x³

basically the test to find out if it is odd is to replace x with - x and if you get the negative of the function then it is odd

basically f (x) is odd of f (-x) = - f (x)

the graph of an odd function is reflected across both the x and y axis to get the other side