Sunday, March 15, 2009

It's The BOB To My Heart :D

I was meaning to do this earlier but since we haven't had the test yet I'm good. xD

How I feel about this unit on a scale of 1-to-10 ? About an 8.5. I understand it, it's just that I make a lot of stupid mistakes... and I mean.. A LOT. The only real trouble that I can foresee is most likely the word problems and some reciprocal graphs. Actually just the word problems because sometimes I just don't read the problem right. =/

Here's basically what I (and you guys too!) need to know:

f(x)=A(Bx-C)+D

Parameter A: Stretches the graph vertically by a factor of a.
Parameter B: Stretches the graph horizontally by a factor of 1/b. Say if the value was 2, then the x coordinates would be multiplied by 1/2.

Parameter C: Moves the graph horizontally C units. WATCH OUT FOR THE SIGN OF C. When it is negative you move the graph to the right and vice versa.
Parameter D: Moves the graph vertically D units.

ALWAYS DO STRETCHES BEFORE TRANSLATIONS!! Just saying... ;)

In the case of trig equations (which you most likely need to know for the word problems)...

g(x)=AsinB(x-C)+D

Parameter A: Is the amplitude (the distance away from the sinusoidal axis).

Parameter B: IS NOT THE PERIOD! B determines the period with the little equation Period=2(pi)/B.
Parameter C: Shifts the graph C units. Watch out for the SIGN! :)
Parameter D: Shifts the sinusoidal axis up or down D units. (This is the average point between the max and min of the graph).

Also.. know how to figure out if a graph is odd or even (or neither!) Just plug in -x and see what you get ;)

When it is even f(-x)=f(x).

When it is odd -f(x)=f(x)

And when it's neither.. well.. its neither of those...

Also know how to graph reciprocal and inverse functions. THESE ARE NOT THE SAME GRAPHS. f^-1(x) DOES NOT EQUAL 1/f(x).

To graph the inverse of f(x) just basically switch the x and y values. Remember to find the invariant point and make sure your sketch goes through it =/ This graph should look like it's reflecting itself over the graph of y=x.

As for reciprocal graphs.. first you have to find the invariant points (where f(x)= 1 or -1). Then look for the asymptotes, then do the 'biggering and smallering' method. :D

I think that's it. It better be. Anyways, I hope we all do really good on the pretest and test :D

Break a pencil everyone~!