Making Connections between Exponential Functions and Logarithmic Functions

Function 3: Look at the equation, graph, and table of Function 3 (with a restricted domain).

Interactive exercise. Assistance may be required. Use the equation and graph of the inverse of Function 3 to complete the ‘Table of Inverse’ below. Complete the table using your own paper.

Function 3
Equation y = 2x + 3

Graph of Function

Inverse of Function 3
Equation y = log2(x - 3)

Graph of Inverse

Table of Function

Table of Inverse

In your notes, answer the following questions.

  1. How does the table of Function 3 compare with the table of the inverse of Function 3?
    2. Interactive popup. Assistance may be required.

    Check Your Answer

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

    Check Your Answer

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

    Check Your Answer

    • Domain: {x|x ≥ 4}.
    • Range: {y|y > 0}.
    Close Pop Up