Introduction to Transformations of Functions

Learning Objectives

By the end of this lesson, you will be able to:

  • Graph functions using vertical and horizontal shifts.
  • Graph functions using reflections about the [latex]x[/latex] -axis and the [latex]y[/latex] -axis.
  • Determine whether a function is even, odd, or neither from its graph.
  • Graph functions using compressions and stretches.
  • Combine transformations.
Figure_01_05_038

Figure 1. (credit: “Misko”/Flickr)

We all know that a flat mirror enables us to see an accurate image of ourselves and whatever is behind us. When we tilt the mirror, the images we see may shift horizontally or vertically. But what happens when we bend a flexible mirror? Like a carnival funhouse mirror, it presents us with a distorted image of ourselves, stretched or compressed horizontally or vertically. In a similar way, we can distort or transform mathematical functions to better adapt them to describing objects or processes in the real world. In this section, we will take a look at several kinds of transformations.