Honors Algebra II



Algebra II--Notes on Logarithmic Functions Name ______________________________

Parent function:

Work with graphing calculator to do the following tasks:

1. Graph parent function: y = [pic]log(x).

2. What is the asymptote? ______________

3. What is the Domain? _____________

4. What is the Range ? _____________

Graph the parent and each of the following functions on your calculator. Describe the changes.

Part A:

1. y = log(x) + 3 ____________________________________________________________

2. y = log(x) - 5 ____________________________________________________________

What can you say about values added/subtracted outside of the function?

______________________________________________________________________________________

Has the asymptote changed? ________________________________

Part B:

3. y = log(x + 2) ____________________________________________________________

4. y = log(x – 8) ____________________________________________________________

What can you say about values added/subtracted inside the function?

_________________________________________________________________________________________

Has the asymptote changed? If so, how? _______________________________________________________

Part C:

Now describe the changes if Part A and B are put together. Also, list the asymptote equations.

5. y = log(x + 2) - 5 ____________________________________________________________

6. y = log(x – 3) + 7 ____________________________________________________________

Part D: Now put in these functions and describe the changes

7. y = 5 log(x) ____________________________________________________________

8. y = 1/3 log(x) ____________________________________________________________

9. y = - log(x) ____________________________________________________________

What can you say about values multiplied outside the function? What about the asymptote?

_______________________________________________________________________________________

Part E: Describe the changes that will take place from the parent graph. List any asymptotes.

10. y = 5 log(x) + 3 ____________________________________________________________

11. y = -2 log(x-4) ________________________________________________________________

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