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Lesson 7

1. Lesson 7

1.9. Explore 5

Mathematics 30-2 Module 7

Module 7: Exponents and Logarithms

 

In Try This 3, you reviewed the characteristics of exponential and logarithmic equations and their graphs. These characteristics are summarized in the following table. You used these characteristics to match equations to their graphs.

 

  Form y-intercepts x-intercepts Graph Increases Graph Decreases
Exponential Functions y = a(b)x one y-intercept that equals the a-value no x-intercepts If b > 1, the graph is increasing. If 0 < b < 1, the graph is decreasing.
Logarithmic Functions y = a + b ln x no y-intercepts one x-intercept If 0 > b > 1, the graph is increasing. If 0 > b < 1, the graph is decreasing.

Self-Check 3


glossary
  1. Complete question 1.a. on page 466 of the textbook. Answer
  2. Match the given functions with the appropriate graphs. Provide an explanation for your choice.

    i. y = 3(2)x ii. y = 5 log2 (x) iii. iv. y = −2 log5 (x)



    1. This is the graph of a function that increases logarithmically and passes through the point 1 comma 0.

    1. This is a graph of a function that decreases logarithmically and passes through the point 1 comma 0.


    1. This is a graph of a function that increases exponentially and passes through the point 0 comma 3.

    1. This is the graph of a function that decreases exponentially and passes through the point 0 comma 5.

    Answer

glossary

Add the following terms to your copy of Glossary Terms:

  • natural logarithm
  • logarithmic regression