Lesson 2

In the next section of the lesson you will study the properties of the graphs of absolute value functions. You will compare these properties to those of linear functions and quadratic functions.

 

Try This 3

 

Part A: Properties of the Absolute Value of a Linear Function

1. Retrieve your graph from Try This 2.
   
   
2. Identify the properties listed in Table 2 for each function. Complete the table.
   
   
    

   Table 2: Properties of y = f(x) and y = g(x)
   	y = f(x)	y = g(x)
   Domain
   Range
   x-intercept
   y-intercept

   
   
   
3. Compare and contrast the properties of y = f(x) and y = g(x).

Part B: Properties of the Absolute Value of a Quadratic Function

4. Identify the properties listed for each of the quadratic functions in Table 3.
   
   
    

   Table 3: Properties of Quadratic Functions
   	y = x2	y = x2 − 4	y = x2 + 4
   Domain
   Range
   x-intercept
   y-intercept

   
   
   
5. Identify the properties listed for the absolute value of each function listed in Table 4.
   
   
    

   Table 4: Properties of the Absolute Value of Quadratic Functions
   	y = |x2|	y = |x2 − 4|	y = |x2 + 4|
   Domain
   Range
   x-intercept
   y-intercept

   
   
   
6. Compare and contrast the properties of the functions in Table 3 and the corresponding absolute value functions in Table 4.
   
   
7. Graph the following pairs of graphs.
   
   
   1. 
   2. 
   3. 
      
      
8. Based on your observations, when is the graph of y = f(x) identical to the graph of ?

Save your answers in your course folder.

 

Share 2

 

With a classmate, compare your responses to Try This 3. Answer the following questions.

1. How do the properties of y = f(x) compare to those of ?
   
   
2. What other properties of absolute value functions can you identify?

Make any necessary revisions to your own work based on the discussion. Save your work in your course folder.