Is the relationship between the side length of a square and the area of the square an example of a function?

Yes. to find the area of a square when you know one side "s", you simply square that side since the area is equal to the base times the height, and the base and height will always be equal in a square since the sides are equal:

A = s^2 

Represented in a function form:

f(s) = s^2

This means whatever you plug in for s, you will square it to get the area.