Parallel functions.

Solution 1:

Now that André has already told you about parallel/offset curves, I am writing this post to drive a certain point home: the parallels of a function may not be functions themselves. To illustrate this point, I will show a family of parallel curves for four common functions:

Note that each family of parallels has at least one member that possesses a cusp, and a point of self-intersection. Some of them might be functions themselves (though the likelihood of them possessing a simple $y=g(x)$ formula is not too high), but generally speaking, parallels are not functions.

Solution 2:

You are looking for the parallel curves to a given curve. The link shows you how to obtain these curves for curves given parametrically.