Making Connections between Exponential Functions and Logarithmic Functions

Function 1: Look at the equation, graph, and table of Function 1 (with a restricted domain). Use the equation and graph of the inverse of Function 1 to complete the ‘Table of Inverse’ below.

Interactive exercise. Assistance may be required. Complete the table using your own paper. You can check your answers by moving your mouse over the table.

Function 1
Equation y = 2x

Graph of Function

Inverse of Function 1
Equation y = log2x

Graph of Inverse

Table of Function

Table of Inverse

In your notes, answer the following questions.

  1. How does the table of Function 1 compare with the table of the inverse of Function 1?
    2. Interactive popup. Assistance may be required.

    Check Your Answer

    • The x-values in Function 1 are the same as the y-values in the inverse of Function 1.
    • The y-values in Function 1 are the same as the x-values in the inverse of Function 1.
    Close Pop Up
  2. What is the domain and range of Function 1?
    3. Interactive popup. Assistance may be required.

    Check Your Answer

    • Domain: {x|x > 0}.
    • Range: {y|y > 1}.
    Close Pop Up
  3. What is the domain and range of the inverse of Function 1?
    4. Interactive popup. Assistance may be required.

    Check Your Answer

    • Domain: {x|x > 1}.
    • Range: {y|y > 0}.
    Close Pop Up