Friday, January 23, 2009
Thursday, January 22, 2009
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 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
Wednesday, January 21, 2009
More about Rational Functions
Hi! everyone..
Sorry for the delay I almost forgot that I have to scribe for today's class.
Today, Mr.K reviewed about the Graphing Function that we did for yesterday's class.
Remember: The seven steps of doing the Graphing Function;
1st step: find the y-intercept
2nd step: Factor (if it can be factor)
3rd step: Find the Roots
4th step: Find the V.A (vertical analysis)
5th step: Find the H.A (Horizontal analysis)
6th step: Sign Analysis
6th step: Sign Analysis
7th step: Sketching the graph
Mr. K ask to do this question:
If the graph didn't touch the x-axis then it doesn't have roots
Mr. K give an example of irrational number that can be factor
don't forget to do the exercise review^_^
next scribe will be EchizenR18
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!
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!
Tuesday, January 20, 2009
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
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.
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
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