Exponential+and+Logarithmic+Functions

Exponential and Logarithmic Functions

1. Collaboratively select one of the big ideas of the Exponential and Logarithmic Functions strand:

**Identify and describe some key features of the graphs, make connections among the numeric, graphical, and** **algebraic representations** **of functions, and solve related problems graphically** 2. Create 5 open questions. Everyone take a look at the questions and make any changes they feel fit. I will be back at 7:45 and will then post the final questions by 8:00. I just want to give everyone a chance to respond to what's here first.

Proposed questions:

1. Construct an exponential equation and a logarithmic equation that have the same transformation/translation and graph them. 2. Draw a logarithmic graph that is increasing or decreasing and goes through the point (100, -2). Write logarithmic function that could be represented by your graph. 3. Draw a graph of an exponential function that grows quickly and one that grows slower. What are the equations of the exponential functions? 4. The function f(x)=logx is transformed by translating to the right and then vertically stretching. Draw the new function on the graph. What is the equation of the new function? 5. Record two important features of exponential growth and suggest two of your own examples of exponential growth. (include graphs)

[Jamal - I like the question above. Question 1, 2 and 5 are good questions in my opinion] Nick - They look good to me [Jamal - They look god to me as well Nick. I wonder if other feel this way.] [Ann: They look good to me too.]

The following three questions are based on the first strand: 1. What are the connections between the laws of exponents and the laws of logarithms? 2. There are two situations that will result an error in the calculator. Why is not possible to determine log (– 3) or log 0? Explain your reasoning. [Kaya: How about "Fill in the blank: log _ = ERROR. Explain." If different students do this question and explain their different answers to each other the different possibilities will be addressed and the sharing makes students feel important.] [Jamal: I actually like your idea. It gives students an opportunity to figure out what the error would be on their own.] [Ann-I like Kaya's idea too} 3. What are the connections between related logarithmic and exponential equations? [Ann: Based on our new big ideas, this don't even need to be exponential equations, we can use any equations] [Jamal - so the question should be "What are the connections between related logarithmic equations?" Would that work based on the big idea. 4. Construct an exponential equation and a logarithmic equation that have the same transformation/translation. This is a great open question because you'll get a ton of different answers for students. 5. Record two important features of what you understand by exponential growth and to suggest your own examples of exponential growth. (Nick)

6. (Kaya) Parallel task: Draw a logarithmic graph that is decreasing and goes through the point (100, -2). OR Draw a logarithmic graph that is increasing and goes through the point (100, -2). Common Questions: 1. How do you know if your graph is increasing or decreasing? 2. Does your graph have an asymptote? What is its equation? 3. Write logarithmic function that could be represented by your graph. 4. How can you check that your function represents the graph you have drawn? 5. Pick a transformation (a specific reflection, translation, or dilatation) and apply it to your graph, sketch the new graph that is produced. 6. What is the logarithmic function represented by your new graph? Parallel tasks are a different strategy then open questions.

To make it open let's do this... Draw a logarithmic graph that is increasing or decreasing and goes through the point (100, -2). Write logarithmic function that could be represented by your graph. This will allow for many possible equations, therefore making it open to every student.

7. Draw a graph of an exponential function that grows quickly and one that grows slower. What are the equations of the exponential functions? 8. Graph y= and x = y[Jamal] 9. {Towhid} Teach students using graphing calculator or softwre and make sure if they knw how to graph simple to complicated exponential and logarithmic functions? 10. {Towhid} How could we relate exponential function in real life financial growth using compound interest, amortization, general annuities, capital budgetig, depreciation, contingent payment, life insurance etc.