Monday, October 26

Homework day. All I did today was start into my acceleratd math and plugged my way through the identities section. not much help need there but alot of work is needed. the day before. which was thursday (no friday due to SAG day) i had to post for the class, so i had no post for the day.

Identities-3

today we took a more back door approach to concept of identities, we solved a few problem, but rather than using formulas we used our knowledge of previous units over the years. We also did some work with extraneous solutions and squareroots and powers. the thing to remember with a root problem is that there is going to be a plus andminus solution. this happpens cause in a square problem there two negatives will equal to what two positives equal. *sigh* now there a mouthful. anyways when you get you answere you will have to check all over them, cause some wont work, but seem to work.

Identities-2

Posted below are the rules, I will try hard to memorize these as this is the section that I dislike most in this course. the trick is to do anything that will eventually lead to the question getting simpler, which in turn will become equal to the other side. It doesn't have to be anything that confusing but even the smallest changes can do alot in the end.

Identities

I believe that an identity are two different problems, related to trig, that in the end they will be equal to each other. The questions on either side of the equals sign may not look similar but are same sames, just different versions. Identities work for any value of any value. they will always work no matter what the inputs are.

DEF. an equality (trigonometric) that evaluates as true for any value of input, that is both sides of the trig. equations are true for ALL possible variables.

*note...trig equations that are not identities are conditional equations....*

trig identities are much like a logic sequence that we learned about many many years ago. ex, if a=b and b=c, then a must = c. it is a simple concept until you start applying it to trigonometric sequences. the harder part of this it trying to understand is that the sequence and everything in the question has a numerical value.

Absolute Values (graphing)

Piece-Wise Function - different rules or outputs depending on relative domain values

absolute values can be understood as piece wise functions.

absolute values on a graph look much like a bouncing ball. But instead of a ball bouncing on the ground, it is a function bouncing along the x-axis. absolute values are actually quite simple, but more complex questions can get quite confusing. The trick to remember here is to take the question one part at a time. and end up at the answer rather than start there. first work with parent function, then add in all the negatives and brackets, inverses and reciprocals, then finally find the absolute values of everything you have got so far.

Reciprocal Functions

Recripocal functions can be defined as;

a/b --------> b/a

In today's class we learned the basics of a reciprocal function. We were refreshed using some grade 11 examples, taught that a reciprocal function is one in which the numerator and denominator switch places, and learned algebraically how to do this. The tricky part come when we put this thing onto a graph!! The graph of a Reciprocal function, compared to it's initial function is curved and has one or more asymptotes along the x axis. first, The asymptote of the reciprocal function is found where the initial function crosses over the x axis (the x intercepts). Near each asymptote the reciprocal function behaves in a manor opposite to the initial function. If the initial function increases as it approaches the asymptote, the reciprocal function will curve off and get smaller and approach the asymptote. Similarly if the initial function decreases, the reciprocal function will increase. The terminology given to was GREATERING and LESSERING. the most important part to remember when deciding whether each function greaters or lessers it to read in the same direction to or from the asymptote. If you read it differently and switch directions at any time, none of the graph will be correct.

Flips, and Symmetry (Even, Odd)

function=vertical line test

inverse function= horizontal line test.

Now this is where it gets difficult, i am going to take some of the screenshots from the lesson today just as a reminder for the next test and so i can view them at home at a later time. This is just basic algebra, but in the end we have to apply it to some set rules that we learned today (ref to screen shots), in all honesty i haven't really caught on to any of this stuff last semester, and it is still confusing at this point. I think the only way to do well on this part of the unit is to memorize the rules and keep going over them even after the class is over. Here is what i got out of today's class:

. -f(x) is different from f(-x)
. The difference is how it is reflected (over x axis and y axis respectively)
. a inverse function is reflected over the line y=x
. EVEN function have symmetry over the y axis (flip symmetry)
. ODD functions have symmetry about the orgin (rotational symmetry)

I still am not to sure how to do the algebra parts and the comparing but i shall research that tonight and refer back to the notes tomorrow!

transformation

Horizontal Compression/Vertical stretch:

a)y=3abs(x) - 3 times as vertically stretched
b)y=1/2abs(x) - 1/2 as vertically compressed

*the "A" value is what is affecting the vertical compression and stretching*


c)y=abs(3x) - 3 times as horizontally compressed
d)y=abs(1/2x) - 1/2 as horizontally stretched

*the "B" value (inside brackets) affects the horizontal compression and stretching*

Summary:
The hardest part to remember is whether it is horizontal or vertical, and today I learned which terminology to use in that certain circumstance. the absolute value refers to the value inside the brackets always being a positive value. This class was mostly a refresher, and it was useful to learn the terminology.

Unit 2 "Transformations"

Terminology:

Translation-"Every point in the relation moves same direction, same distance in a plane." y=f(x-h) - left and right, y=f(x)+k - up and down. it is moved either up down, left right, or a combination of the two.(which can be viewed/seen as a diagonal shift)

So we had our first unit test yesterday, therefore I had no post. In my opinion I found it to still be on the more difficult side, but this time i had the skills to look a little deeper that just the question itself. I could see the unit circle much more clearly this time around, and it help in more ways than I would have though possible. So I am hoping for the best on this one, and hopefully my class is of to a good start!!