Module 6: Lesson 4

 

Self-Check 1
  1. Questions 1.b. and 9 on page 380 of the textbook
    1.  
      1.  
        1. The graphs of the equation and its inverse are as follows:

           
          This is a graph of two functions as well as the image line y equals x. One function is y equals one-third to the exponent x; the other function is the inverse of the original function.
        2. The function is

          To find the inverse, switch the x and y variables.

           


          Then write in logarithmic form.

           


          The equation of the inverse of the function is
        3. The inverse function of the graph has the following characteristics:
          • The domain is {x|x > 0, x ∈ R}.
          • The range is {y|y ∈ R}.
          • The x-intercept occurs at (1, 0).
          • The y-intercept does not exist.
          • There is a vertical asymptote with the equation x = 0.
    1.  
      1. The function is the same as

        To find the inverse, switch the x and y variables.

         


        Then write in exponential form.

         


        If then
      2. The sketch of the two functions is as follows:

         
        This is a graph of two functions as well as the image line y equals x. One function is at y equals the logarithm with base of one-fourth at x; the other function is at y equals one-fourth to the exponent x; the two functions are inverses of each other.

        The inverse function of the graph has the following characteristics:
        • The domain is {x|x ∈ R}.
        • The range is {y|y > 0, y ∈ R}.
        • The x-intercept does not exist.
        • The y-intercept occurs at (0, 1).
        • There is a horizontal asymptote with the equation y = 0.


© 2012 Alberta Education