Lesson 4

Turn to “Example 1” on pages 394–395. Compare the solution presented in the textbook to your answers from Try This 2. Make any necessary revisions to your own work as you confirm your understanding of the concepts. Pay careful attention to the following elements of the solution:

• Look carefully at the graph along the y-axis. What do you notice? What do you think is the significance of that part of the graph?
  
  
• What is the end behaviour of each graph?
  
  
• What do you think is meant by invariant points?

Self-Check 1

1. A function is defined as f(x) = 3 − 2x. Which of the following is the reciprocal, g(x), of this function?
   
   
   1. 
      
      
   2. 
      
      
   3. 
      
      
   4. 
      
      
   Answer
   
   
2. Which of the following is the equation of the vertical asymptote for the function ?
   
   
   1. 
      
      
   2. 
      
      
   3. 
      
      
   4. 
      
      
   Answer
   
   

3. Two functions are defined as f(x) = x2 + 9x + 20 and g(x) = x2 + 3x − 10.
   
   The graphs of the reciprocals of f and g share a common vertical asymptote. Which one of these equations does this asymptote have?
   
   

   1. x = 5
      
      
   2. x = −5
      
      
   3. x = 2
      
      
   4. x = −2
   
   Answer