Logarithmic Functions Unit Plan
Discovery Based Learning
1. Algebra 2: What is Log? -- TInspire Activity
This lesson involves the one-to-one function f(x)=bx. In acknowledging the existence of its inverse, students will:
- Use the domain and range of f(x) to determine the domain and range of f-1(x).
- Interpret the graph of f-1(x) as the reflection of f(x) across the line y = x.
- Use this inverse relationship to write an equation for the graph of the inverse.
- Recognize the logarithmic notation needed to define the inverse function.
- Use the inputs and outputs of two inverse functions to complete a table. As a result, students will:
- Solve simple logarithmic equations and verify solutions using the corresponding exponential equations.
2. Graph Logarithms -- TInspire Activity
Students will investigate the graphs of the family of logarithm functions f(x)=loga(x), by changing the a-value over the interval 0 less than or equal to a less than or equal to 4. As a result, students will:
- Infer why the conditions a>0 and a≠1 are necessary.
- Determine how the value of a affects the increasing or decreasing behavior of the function.
- Determine the x-intercept, domain, range, and asymptotes.
- Describe the end behavior. NOTE: The time varies for this activity depending on whether students create the TI-Nspire document or use the pre-constructed .tns file.