In Try This 2 you will further explore when asymptotes occur and when points of discontinuity occur.

 

Try This 2

 

Consider the following two rational functions:

 

1.  
   1. Determine the non-permissible value for f(x) and g(x).
   2. Graph f(x) and g(x) using technology and make a sketch of the graphs.
   3. Use your graphs to complete a table like the following.
      
      

      	f(x)	g(x)
      Non-permissible Value
      Description of Graph at Non-permissible Value
      Description of Graph Near Non-permissible Value

2. Try to explain why a point of discontinuity occurs in f(x) and an asymptote occurs in g(x).
3.  
   1. Factor the numerator and denominator for both functions using common factors.
   2. Cancel any factors that appear in both the numerator and denominator.
4. Revise your explanation for question 2, if necessary.

  Save your responses in your course folder.

 

Share 1

With a partner or group, compare, share, and discuss your responses to Try This 2. Based on your discussion, develop a general statement describing how to determine if a non-permissible value is indeterminate or undefined. How does this relate to factors in the numerator and denominator?1

 

If required, save a record of your discussion in your course folder.

 

1 Source: Pre-Calculus 12. Whitby, ON: McGraw-Hill Ryerson, 2011. Reproduced with permission.