Module 6: Exponents and Logarithms

 

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Try This 1
  1. State the inverse of f(x) = 5x.
  2. Complete the following tables of values.

    f(x) = 5x

    x

    y

    −2

     

    −1

     

    0

     

    1

     

    2

     

    INVERSE OF f(x) = 5x
    f -1(x)

    x

    y

     

    −2

     

    −1

     

    0

     

    1

     

    2
  3. Sketch the graphs of f(x) = 5x and the inverse, f −1(x).
  4. Identify the following characteristics of the graph of f(x) = 5x and the inverse graph.

    Characteristics f(x) = 5x f -1(x)

    Domain

    		    

    Range

    		    

    x-intercept

    		    

    y-intercept

    		    

    Equation of Any Asymptotes

    		    
  5. Open “Logarithmic Functions – Activity A.”

     

     
    This is a play button that opens “Logarithmic Functions – Activity A.”
    Screenshot reprinted with permission of ExploreLearning


    Step 1: Change the a-value to 5.

    Step 2: Click on the box “Show associated exponential.”

    Step 3: Click on the box “Show line y = x.”

    Step 4: Compare your answers to Try This 1 to the graphs produced.
  6. How are the x- and y-coordinates of the corresponding graphs related for the two functions?
  7. Describe the transformation of the graph of f(x) = 5x to get the graph of the inverse.

course folder Save your responses in your course folder.

 

Share 1

 

Based on your graphs created in Try This 1, discuss the relationship between the characteristics of the function f(x) = 5x and the inverse, f –1(x), with a partner or group.

 

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

Remember that logarithmic functions are the inverse of exponential functions. First change the function to y = 5x , and then switch the x- and y-variables. Isolate y by using logarithmic form.