Look at the equation, graph, and table of Function 4 (with a restricted domain).

Interactive exercise. Assistance may be required. Use the equation and graph of the inverse of Function 4 to complete the ‘Table of Inverse’ below. Complete the table using your own paper.

Function 4
Equation y = -2x - 1

Graph of Function

Inverse of Function 4
Equation y = log2(-x + 1)

Graph of Inverse

Table of Function

Table of Inverse

In your notes, answer the following questions.

  1. How does the table of Function 4 compare with the table of the inverse of Function 4?
    2. Interactive popup. Assistance may be required.

    Check your answer

    • The x-values in Function 4 are the same as the y-values in the inverse of Function 4.
    • The y-values in Function 4 are the same as the x-values in the inverse of Function 4.
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  2. What is the domain and range of Function 4?
    3. Interactive popup. Assistance may be required.

    Check your answer

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

    Check your answer

    • Domain: {x|x < – 1}.
    • Range: {y|y > 1}.
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  4. What conclusion can you make about the domain and range of an exponential function and its corresponding logarithmic function?
    5. Interactive popup. Assistance may be required.

    Check your answer

    • The domain of the exponential function becomes the range of the logarithmic function.
    • The range of the exponential function becomes the domain of the logarithmic function.
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