Exponents and Logorithms

Today we had a double class for precal. This was the first class we had about logarithms. Honestly I didn't find it to difficult at the beginning but once we started to get into it I was in a loss for words. Here's how the morning went.

First we looked at how to find the :


1)domain & range
2)horizontal asymptote
3)x & y intercepts of the graph
4)sketching the graph



1) To find the domain and range we look at the graph and see how far the graph stretches on the x axis. For this function the graph is going to negative infinity and to infinity.

2) The horizontal asymptote for this graph is y=0. This is because the function will never touch 0. The line y=0 is the x axis.

3) This function has no x intercepts because it will never touch the x axis. The y intercept of this function is 1/4 because to find the y intercepts we let x=0.
-2^(x-4)

x=1/4

4) To sketch the graph we sketch the graph of 2^x and just move it 2 units to the right.

After that question we did a similar one to it except there was another wrinkle added.

g(x)=-2^(x+2)




I wont explain this one is detail since it is similar to the first one. However in this one there is a negative infront of the 2. Here we have to look carefully and see that there are no brackets with the negative. Therefore we have to work on the exponent first.

2^(x+2)
Then we add the negative sign afterward.

I cant remember if this was in the afternoon class or not but he gave us a table and wanted us to find the inverses for each function.





I believe that this wasn't a very hard concept. Basically we just plug in the x value and find out what the result is. For the green graph we took the inverse of the other graph.

Then we looked at flipping a graph over the y=x line.



To graph a function over the y=x line you must switch the x values with the y values.



Then next came the most important part. We learned that logarithms are exponents. If you learned anything today, always remember that logarithms are exponents.





After we learned that logarithms are exponents we did a few questions on turning a log into an exponent.













I'm going to insert a slide in that space. Some reason it isn't working now. So I'll end it for now until I get home. Remember the LOGARITHMS ARE EXPONENTS* The scribe for tommorow will be Oliver.