Sections 2.6 - Graphs of Special Functions; Translations

Section Objectives

  1. Sketch the graph of .
  2. Use basic translations to sketch graphs.
  3. Sketch the graphs of square root and cube root functions.
  4. Sketch the graphs of shifted parabolas.

Graphing basic cubic functions

Like lines and parabolas, the graphs of functions of the form are part of our collection of basic college algebra graphs. Before plotting any points, we can actually notice a few very important features of the graph:

With these ideas in mind, it takes only a few plotted points to obtain a very nice graph.


The graphs of the basic square root and cube root functions

Just as we analyzed the graph of before we even started sketching it, we could similarly think about the graphs of and .

Here is the graph of .

And here is the graph of .

These graphs should join our collection of basic graphs.

Translations of graphs

The following ideas will help us to easily obtain the graphs of more complicated functions from our basic graphs.

Suppose that we have the graph of the function and that is a positive number.