Lesson 2

Absolute value functions have the form , where f(x) is a function.

Retrieve the results from the Discover section. In that activity you discovered that the graphs of absolute value functions are found either on or above the x-axis. In Try This 2 you will use tables to find out why.

Try This 2

Consider the functions f(x) = x − 2 and .

1. Determine the y-coordinates for each of the given x-coordinates in each function. Record your answers in a table like the one that follows.
   
   
    

   Table 1: Table of Values for y = f(x) and y = g(x)
   x	y = f(x)	y = g(x)
   −6
   −3
   0
   3
   6

   
   
   
2. Plot the ordered pairs for each function on the same graph paper.

Save your work in your course folder. Save Table 1 for future reference.

Share 1

With a classmate, discuss the following questions based on Try This 2.

1. Compare your answers in the second and third columns of Table 1. When are the values the same? When are they different?
   
   
2. Based on Table 1 and the graph, explain why the graph of the absolute value function y = g(x) is not found below the x-axis.
   
   
3. Assume that a student chose different x-values for Table 1 (as shown in the following table) to use for sketching the graph of y = g(x).
   
   
   
    

   x	y = f(x)	y = g(x)
   2
   3
   4
   5
   6

   
   
   
   1. How could this selection of x-values lead the student to an incorrect graph?
      
      
   2. How do you choose values of x so that you do not sketch an incorrect graph?

Save your responses in your course folder.