Module 3 Group Activity: Exploring Exponential and Logarithmic Functions

COMPLETE ME FIRST

In the space below, please enter your: [br]1. First Name[br]2. Last Name[br]3. Group Number

The colored letters on the right hand side are called parameters. Slide the dots or type in numbers and see their effect on the graphs.

Activity Directions:

The graphs above are inverses of each other. [br]The gray graph is the logarithmic graph, and is labeled as [math]g\left(x\right)[/math],[br]The orange graph is the exponential function, and is labeled [math]g^{-1}\left(x\right)[/math].[br]When I ask about the logarithmic or exponential function, it may be helpful to click the checkbox associated to the other function so you can see how the parameters affect each graph separately. [br]When you click on the checkbox, all objects associated with that graph will also appear/dissappear. [br][br]Use the directions below to guide your thinking BEFORE answering the questions below.[br]Change the parameter, [i]a[/i]. [list][*]What is this number called? [/*][*]How does it change the graph of [i][i][i][i][i][math]g\left(x\right)[/math][/i][/i][/i][/i][/i][i], [/i]the logarithmic function?[/*][*]How does it change the graph of [math]g^{-1}\left(x\right)[/math], the exponential function?[/*][/list]Change the parameter, [i]k[/i][list][*]How does it change the graph of g(x), the logarithmic function?[/*][*]How does it change the graph of [math]g^{-1}\left(x\right)[/math], the exponential function?[/*][/list]Change the parameter, [i]d[/i][list][*]How does it change the graph of g(x), the logarithmic function?[/*][*]How does it change the graph of [math]g^{-1}\left(x\right)[/math], the exponential function?[/*][/list]Change all three parameters. [br][list][*]Write down the functions in your notes[/*][*]Draw the graphs underneath in your notes[/*][*]Label the graphs, vertical and horizontal asymptotes, and points.[/*][/list][br]

1. How does changing the parameter "a" affect the graph of the logarithmic function vs the graph of the exponential function?

2. How does changing the paramter "k" affect the graph of the logarithmic function vs the graph of the exponential function?

3. Given the information below, describe what the graph of f(g(x)) and g(f(x)) would look like. [Hint: How would you show that f(x) and g(x) are inverses?]

Given [math]f\left(x\right)=e^x[/math] and [math]g\left(x\right)=ln\left(x\right)[/math], describe the graph of [math]f\left(g\left(x\right)\right)[/math] and [math]g\left(f\left(x\right)\right)[/math] read as f composed of g(x) and g composed of f(x), respectively.