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Wednesday, September 17, 2008

Exponentially Exponentializing Exponential Functions Exponentially

Hey the Benchmeister here and this will be my first AP Calc post this year. Today we began on exponential functions if you haven't found that out from my title :P. Okay we were given a worksheet to work on during class. The worksheet can be found on today's slides (Just click on the slide to enlarge).

For exponential functions the y-intercept is represented by a in the form a * b^x. This is because the x-coordinate of any function is 0 (zer0). So by substituting 0 for x, b will be 1 because any base to the exponent of 0 will be 1. Thus leaving us with a. In the worksheet a term called the growth factor is used. The growth factor is the common ratio between the outputs. For example what common factor do you have to multiply the previous output to get the next output. The growth factor is represented by b in the form above.

We then moved onto the next unit: Inverse Functions. The following link will show Mr. K's way of explaining Inverse Functions:
Well an inverse function is a function that undid what the original function did. If the original function was y = x - 1. Then the inverse would be found by switching the x and y around getting x = y - 1. Then just solve for y and you get the inverse. Also for an inverse all the ordered pairs of a function are switched. In a graphical view, the inverse of a function is the original function reflected over the line y=x.

Well that's all. Homework is Chapter 1.6, odd questions between 1-9 (including 9). But by the looks of it all of them are doable. :D

The next scribe will be le jos├ęph.

This is your local cuddle monster logging off.

And if you haven't tried solving my math fun CLICK HERE

1 comment:

Dr. Eviatar said...

Great post, Benchman! I challenge you to say your title three times fast tomorrow in class, though.

I love all these links back to the past - I really, really want to be like Mr. K when I grow up. I'm counting on you guys to help me.

Sorry we are being kind of mechanical and work-sheety right now. I'll try to remember the block of wood.