The rational function f(x) = a over x - h a (x – h) + k and the square root function f(x) = a√(x – h) + k can be transformed using methods similar to those used to transform other types of functions.

Let’s begin by reviewing the rational and square root parent functions. Notice that the graphs of both parent functions are either centered or begin at the origin.

In the following sections, you will investigate each of these function families and the effects of changes to a, h, and k using graphs, tables, and verbal descriptions as compared to the parent function.