Objectives
- Students will explore the family of logarithmic functions of the form f(x) = c*logb(x+a) and describe the effect of each parameter on the graph of y = f(x)
- Students will determine the equation that corresponds to the graph of a logarithmic function.
- Students will understand how a vertical shift in the graph of a logarithmic function is related to properties of logarithmic functions.
Vocabulary
- logarithmic function
- natural logarithm
- parameter
- translation
- reflection
About the Lesson
This lesson involves the family of logarithmic functions of the form f(x) = c*logb(x+a).
As a result, students will:
- Manipulate minimized sliders, and observe the effect on the graph of the corresponding logarithmic function.
- Make a general statement about the effect of each parameter on the graph of the logarithmic function.
- Match specific logarithmic functions with their corresponding graphs.
- Relate properties of logarithmic functions to vertical translations of their graphs.
*Note: This activity contains an optional AP Practice Questions document for those students preparing for the AP Precalculus Exam.