Module 2: Radical Functions

 

In Try This 3 you may have noticed that the parameters a, b, h, and k from the general form affect the graph of the radical equation in the following ways.

 

Parameter Value > 0 Value < 0
a Vertical stretch of graph of by a factor of a. Vertical stretch of graph of by a factor of a. Graph of reflected in x-axis.
b Horizontal stretch of graph of by a factor of Horizontal stretch of graph of by a factor of Graph of reflected in y-axis.
h Graph of is translated to the right h units.

Graph of is translated to the left h units.
k Graph of is translated up by k units.

Graph of  is translated down by k units.

 

Self-Check 1
  1. Complete the four questions at the bottom of “Functions Involving Square Roots.” Check your answers.

     
    This is a play button that opens “Functions Involving Square Roots.”
    Screenshot reprinted with
    permission of ExploreLearning.

 

textbook

  1. Complete questions 2.a., 2.c., and 3 on page 72 of the textbook. Answers


Now that you have seen how radical functions can be transformed by different parameters, you will use this understanding to graph transformed radical functions. The following animated examples show two different methods that can be used to graph radical functions using transformations. Do you prefer one of the methods?

 

Method 1: Transform the Graph Directly

 

Go to Graphing Radical Functions by Transforming the Graph.

 

 

This play button opens Graphing Radical Functions by Transforming the Graph.

 

Method 2: Map Individual Points

 

Go to Graphing Radical Functions by Mapping Points.

 

 

This play button opens Graphing Radical Functions by Mapping Points.



textbook

If you would like to review some more examples about how the two methods are used to graph radical functions, read “Example 2” on pages 65 to 67 of the textbook.

 

Self-Check 2
  1. Complete “Your Turn” on page 68. Answer
  2. Complete questions 5.b. and 5.c. on page 73. Answer