Transformations: Parent Function

Transformations

Parent Function

The simplest rational function is called the parent function and is $frac1$ . To understand how to graph a rational function, it is important to understand the shape of the parent function and how it moves. The graph of $frac2$ is shown below:

graph

The parent function has an excluded value of x = 0. Notice that the graph approaches, but never touches the line x = 0, because the function is undefined at that value. This creates a vertical asymptote on the y-axis.

There is also a horizontal asymptote on the x -axis. There is no value of x , for which $frac3$ will equal 0. Therefore, as the value of x increases the value of the fraction approaches zero, creating the asymptote at y = 0.