## Graphing Functions Using Vertical and Horizontal Shifts

In the next few sections, you will begin to strengthen your ability to graph functions without the aid of a graphing tool and without having to do a lot of algebra. You will learn some basic transformations that can be done to the graphs of the toolkit functions to make more complex functions. For example, we can take the graph of the square root function , shift it to the left or right, and determine the resulting equation. Conversely we can begin with the equation of and determine what has been done to the graph of without doing a lot of algebra.

### Transformation of Functions

#### Learning Objectives

In this section, you will:

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

**Figure 1**

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.

Source: Rice University, https://openstax.org/books/college-algebra/pages/3-5-transformation-of-functions

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