Well, you can describe a circle with a single function if you look at a function R -> R^2. But a circle can't be the graph of a single function.

f and g form the top an bottom of the circle. note that they only differ by a single sign

you need two of them because a circle can't be expressed by a single function of x as it needs to map every x value to 0 to 2 y values

A graph is just a series of correlated points, a formula to tell you that when x is set to a certain value y has a different value. It follows then that no single function can define a circle because for every given value of x there would have to be two potential values of y.