A hole in the graph

Hell0 :)

Today in class, we continued doing the unfinished example from yesterday's class. The first thing we did was Mr. k showed us the video of a real "Plug Hole" because it is related to our topic today. Here's what he showed us "Plug Hole (short version)" "Plug Hole (long version)" Feel free to watch it..

Anyways here are the examples we did...













next scribe is Ashley

Today's Slides: January 22

Here they are ...

Pre-Cal 30S January 22, 2009

View more presentations or upload your own.

Today's Slides: January 21

Here they are ...

Pre-Cal 30S January 21, 2009

View more presentations or upload your own. (tags: pc30sf08 precalculus)

Function mix with Niwatori-san XD

Morning fellow Math ELITES!!

Itz function time last unit for this curriculum but not the last for your school year!

T_T

Oh stop crying about it letz go on with some learning!


Well following with the Synthetic division as well as the RATIONAL ROOTS THEOREM . . .
we can get sketching a graph well worth the time to look at. =p


Please follow these steps as followed to sketch the graph!

Step 1: Find your Y-intercept by letting variable X become zero like this
e.g . . . . . (x=0)
Good job you're smart!

Step 2: Find all rational roots possible while reminded to wiping out the copied numbers
(Use the rational roots theorem if needed)
Okay next step!

Step 3: Determine the sign of the function by looking at the different ways the X intercepts are hitting the X-axis such as -2 hitting at X and another hitting +2 see different spots!

Final Step! *Was going to do a drum beat but I let the drum just roll away* Step 4: Sketch the Graph! XP (what did you expect Oprah Winfrey forget it!)


Of course this is done after you get show the work so these following diagrams will show you how:

1st use Synthetic division mind yourself this is to find Polynomial Functions I will touch with Rational Functions in the next one!



Ok, you got the roots time to graph it with the roots acquired!



Use the equation and get the Y-intercept by letting the X's in the equation F(x)=4X^3+3X^2+4X+5
so...
Y = 4(0)^3+3(0)^2+4(0)+5
= 5

After doing this you can make a number line including all the Roots/X-intercepts depending on the context used in this case it's roots for the number line


Sketching Rational Functions is just a bit of an extra step! All that is different is that you need to look for vertical asymptotes.

Asymptotes are lines on a graph not meant to be there but they are there to show that certain part of the Cartesian plain is not allowed to have a(n) point to touch the line. If the point does touch then there is something wrong with the graph.

*Be careful to not mistake the Asymptote as part of the graph itself!*

Oh yes, quick reminder you have to find both horizontal and vertical Asymptotes not just the vertical.

Ok... that was to get the horizontal asymptote but to get the vertical asymptote you just need the root of the denominator!

*****Please notice!!! that not all the time will there be an asymptote!!! So no need to worry if there isn't one present!!!****


Niwatori-san signing off I'll see you all in the next year. Have fun next Pre-cal class and hopes to always to feel happy as well obliged to use your own voice to help out your peers.

"A little voice from you could change a lot from the many in silent"
-By: Niwatori-san- GAMBETE FOLKS!















> . < So sorry people I forgot to scribe the past two times but yeah I had work and even though that be a bad excuse to skip scribing I'm still sorry!

Graphing Rational Functions

This morning we continued talking about Graphing Rational Functions. We went back to the example from yesterday's class and finish graphing the rational function.

Example:

Step 1: Find the y-intercept by letting x=0.



Step 2: Factor everything, which in this case it's already factored.

Step 3: Find the roots of the function by finding the roots of the numerator.
This one has NO ROOTS.

Step 4: Find the vertical asymptotes by finding the roots of the denominator.
V.A. → x=2

Step 5: Find the horizontal asymptotes by dividing each term in the function by highest power of x, and take the limit as x goes infinity.

H.A. → y=0

Step 6: Determine the sign of the function over the intervals defined by the roots (step 3) and vertical asymptotes (step 4).

Step 7: Sketch the graph.

This is not the the exact graph, but it gives us idea on how the graph would look like.

We did another example on graphing rational functions, but it's pretty much the exact same thing on how we solve it. The only thing that changed was the graph (we can see this on the slides that Mr. K post everyday).

Homework: Go back to the Exercise that was assigned yesterday and and do the graphing rational functions part of it. Also, don't forget to start on doing the last exercise in the book that covers all the units that we did in Pre-Cal.

Next scribe is Larlyn

- Jeamille

Today's Slides: January 20

Here they are ...

Pre-Cal 30S January 20, 2009

View more presentations or upload your own. (tags: pc30sf08 precalculus)

Today's Slides: January 19

Here they are ...

Pre-Cal 30S January 19, 2009

View SlideShare presentation or Upload your own. (tags: precalculus pc30sf08)

Today's Slides: January 16

Here they are ...

Pre-Cal 30S January 16, 2009

View SlideShare presentation or Upload your own. (tags: pc30sf08 precalculus)

Today's Slides: January 15

Here they are ...

Pre-Cal 30S January 15, 2009

View SlideShare presentation or Upload your own. (tags: pc30sf08 precalculus)

Remainder Theorem and The Rational Roots Theorem

Today in class, we went over one more time how to do synthetic division and how to find the roots of a function using the Remainder Theorem.

After that, we learned how to find the missing coefficient in a polynomial if we already know what the remainder is. Here's how you would do this:

Let's say you have the question:


The first thing you want to do is write it out in a way that is easy to understand:


Then you plug the root of the denominator into the function:


Since we already know the remainder we can rewrite it this way:


Now all we do is isolate K with a little algebra, and solve it:


And there you have it!

Near the end of the class we managed to quickly learn the Rational Roots Theorem. This theorem allows us to find any rational roots of a polynomial function. Here's an example:

So you're given the equation:


The first thing to do is the find all the possible positive and negative factors of the constant term:


Now we find all the positive factors of the leading coefficient:


We then list all the possible rational roots, eliminating any duplicates:


We can then test out these roots by using synthetic division and the factor theorem to turn the function into a quadratic (Remember: If the remainder is 0, then it is a root):


This then gives you:


Now you just factor the equation and find the roots:


And there you have it! That's about all we did for today, tomorrow's scribe will be...Niwatori-san

Today's Slides: January 14

Here they are ...

Pre-Cal 30S January 14, 2009

View SlideShare presentation or Upload your own. (tags: functions precalculus)

Today's Slides: January 13

Here they are ...

Pre-Cal 30S Jauary 13, 2009

View SlideShare presentation or Upload your own. (tags: pc30sf08 precalculus)

Today's Slides: January 12

Here they are ...

Pre-Cal 30S January 12, 2009

View SlideShare presentation or Upload your own. (tags: precalculus pc30sf08)

Today's Slides: January 9

Here they are ...

Pre-Cal 30S January 9, 2009

View SlideShare presentation or Upload your own. (tags: pc30sf08 functions)

Functions

Hi every one!

I hope everyone did well on the test. Today we started a new unit called Functions. Function is a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another.

We can express functions in ways such as:-

1. sets:- For example A:{2,3,4,5} and set B:{6,7,8,9}.

2. Graphs:- For example this is a graph of the equation f(x)=x^2+2.

3. Formula:- For example f(x)=x^2+2.

We have also talked about relations. Relation is a set of order pairs.
Types of relation functions

1. One-to-one Relation:- this relation is a function because only one element of set A is corresponding another element in set B.



2. One-to-many Relation:- this is not an a function because the element 1 from set is corresponding to 2,4 in set B.


3. Many-to-one Relation:- 3 elements from set A are corresponding to the element 4 in set B which is many to one.



We have also talked about the vertical line test. It is a vertical line that touches the graph only once.
For example this graph is a Function because it touches the vertical line test once.

This one is not a function because it touches the vertical line test twice.

Sources :- http://www.tutorvista.com/content/math/algebra/function/function.php
http://www.purplemath.com/modules/fcns.htm


Next Scribe :- Ale ...

Today's Slides: January 8

Here they are ...

Pre-Cal 30S January 8, 2009

View SlideShare presentation or Upload your own. (tags: precalculus pc30sf08)