## Wednesday, February 25, 2009

### Reflecting on Translations and Transformations

Good evening everybody! It's WonderfullyExcellent, aka Alex. I'd like to start off today's post by saying HAPPY BIRTHDAY JOHN!
Hope you have a good one.

Now, to today's class. We started off right away with translations and transformations. We went through today's slides which were quite helpful and informative. Unfortunately the Internet was down and we could not access Fooplot, but if you were confused about anything try putting it on Fooplot yourself. Another unfortunate occurrence, I can't seem to be able to capture the image of the slides from today, so you'll have to view them yourself too.

What we learned today was pretty much a review of what we already know. Here's a review though:

When f(x)= (x) + 1 then the graph is moved up 1 unit.
When f(x)= (x) - 1 then the graph is moved down 1 unit.

The shift, whether up or down, becomes the new sinusoidal axis.

When f(x)= (x+4) then the graph is moved left, yes left, 4 units.
When f(x)= (x-4) then the graph is moved right, yes right, 4 units.

When f(x)= 2(x) then the graphs amplitude (the distance from the sinusoidal axis) becomes 2 above and below the sinusoidal axis.
When f(x)= -2(x) then the graphs amplitude IS STILL 2, the graph is just reflected (flipped over the sinusoidal axis).

REMEMBER THAT THE AMPLITUDE IS A DISTANCE, SO IT IS ALWAYS POSITIVE, YOU ALWAYS TAKE THE ABSOLUTE VALUE OF THE AMPLITUDE.

Finally, when f(x)= (2x) then the period is changed. To find the period you take the number you have in front of x, in this case 2, and put it under 2pi. This gives you the period.

Remember, when the number in front of x is a whole number, the frequency between 0 and 2pi is increasing. When the number in front of x is a fraction, the frequency is decreasing.

KEEP IN MIND DABC, AsinB(x - C) + D

Now, if you have the function f(x)= (4 - x^2)
and you change it to 2f(x)= (4 - x^2) then you are shifting the amplitude up/down 2 units. Basically you are stretching the graph vertically. Note; this does not affect the horizontal values.

If you change the same function to f(2x)= (4 - x^2) the graph is compressed horizontally 2 units. And if that two was 1/2 then the graph would be stretched horizontally 2 units. Note; this does not affect the vertical values.

After going through the slides, we corrected a portion of our tests, hope everyone did as well as they wanted too. If you have any questions or concerns about the test, post them on the blog or talk to either Mr.K or Dr.E.

Hope everyone found this post helpful, see you all in class tomorrow. Oh! Remember there is a quiz on all this stuff tomorrow, Good Luck.

The next person to have the privilege to scribe for tomorrows class is Jennifer.