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!

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