## Thursday, February 28, 2008

### Transformations

I am deeply sorry I posted so late, and I apologize to whomever was waiting for a scribe post. Unfortunately I didn't check the blog yesterday and hadn't realized that I was the next scribe as I was up working on a project for another class. Anyways, I'll recall as much as I can remember.

We started off the class waiting outside... but then he let us back in and let us write the second half of the test where we drew the graph of a function and wrote two functions for a graph. As you can see in the second slide, we went over the question just in case anyone u, anxieties, questions and any good jokes. In slide three we quickly went over what the answer was for the second question. He showed us a quick process to easily write the function. He found 'D' was 3 because the sinusoidal axis had moved UP 3 units. He found this by looking at the distance from crest to trough and found that distance was 6, so then he discovered D was 3. From that he also concluded that the amplitude was also 3. Finding the period, he saw that one full wave had occurred in the time of 'pi' so then he took B = 2pi/period, and found B = 2, as you can see in the slide. For Sine, there was no phase shift as the graph already started at the origin of the sinusoidal axis. For Cosine, he took the closest maximum value to the Y axis and found the phase shift is pi/4. So now we have the Functions. But don't do what I did and REMEMBER to put either y = 'function' or for whatever function its asking you to find (ex. f(x) = ...) You'll LOSE a WHOLE MARK as it is an EXPRESSION and not a FUNCTION.

We then looked at translations and how 'a' and 'b' respectively affect the function and it's position where 'a' affects the x coordinate and where 'b' affects the y coordinates as you can see in slide 4.
'A' is like the phase shift, and shifts the 'x' position of the function left or right, and b is like the sinusoidal axis, but really it just shifts the function up or down (depending on the sign).

We then looked at stretches. In f(x) = ... x is what is used to graph, so if in the case there is a 2 in the f(x) (ex. f(2x) or you can just look in the slides), the 2 would affect how the function looks. If the two happened to be in front of the whole function, the whole function would be multiplied by two. We then headed over to http://fooplot.com to see how they would get affected by an integer in front of the 'x'. The larger the integer, the smaller the function looks, because in a sense, it takes less time, as to where if it were an integer, that would mean it would take longer, thus stretching the graph out.

Unfortunately we didn't make it to Compressions.

It's probably no-use saying this at this time of the night but homework is exercise 8. Again, I'm truly sorry for posting so late, especially to the people who were looking for the scribe to post to look for some answers.

~Rence_Out

Oh yeah, Next scribe will be... *checks list*

DARTH PAUL! I CHOOSE YOU! QUICK ATTACK, NOW!

To simplify that unnecessary outburst of randomness, Paul's the next scribe.