Discovery Based Learning

1.  Algebra 2: What is Log?  -- TInspire Activity

This lesson involves the one-to-one function f(x)=b^x. 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)=log_a(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.