Problem : For a given value of x and a function f, how many values of f (x) exist?

One. A function is defined such that for any x in the domain of the function, there is only one value f (x) in the range.

Problem : Is the graph below a graph of a function?

Yes.

Problem : Is the graph below a graph of a function?

No, for some values of x, f (x) has two values.

Problem : Is the graph below a graph of a function?

Yes.

Problem : Is the graph below a graph of a function?

No. For some values of x, there are two values of f (x).