Leading coefficient test, Algebra

Assignment Help:

Assume that P ( x ) is a polynomial  along with degree n.  Thus we know that the polynomial have to look like,

                                                    P ( x ) =axn..............

We don't know if there are any other terms in the polynomial; however we know that the first term will need to be the one listed as it has degree n. Now we have the following facts regarding the graph of P ( x ) at the ends of the graph.

1.   If a> 0 and the value of n is even then the graph of P ( x )will increase without restricts positively at both endpoints.  A good instance of this is the graph of x2.

2369_Leading Coefficient Test.png

2.   If a= 0 and the value of n is odd then the graph of P ( x ) will increase without bound positively at the right end and decrease without bound at the left end.  A good instance of this is the graph of x3.

1749_Leading Coefficient Test1.png

3.   If a= 0 and the value of n is even then the graph of P (x ) will decrease without  any bound positively at both of the endpoints.  A good instance of this is the graph of -x2.

900_Leading Coefficient Test2.png

4.   If a= 0 and the value of n is odd then the graph of P ( x ) will decrease without  any bound positively at the right end and increase without  any bound at the left end.  A good instance of this is the graph of -x3.

990_Leading Coefficient Test3.png

Okay, now that we've obtained all that out of the way finally we can give a procedure for getting a rough sketch of the graph of a polynomial.


Related Discussions:- Leading coefficient test

Y=a+bx, how do you solve this#question with (3,5)and (2,1) ..

how do you solve this#question with (3,5)and (2,1) ..

Polynomilas, i dont get them i need help

i dont get them i need help

Matrix, given a matrix "A" determine the matrix represented by -5A

given a matrix "A" determine the matrix represented by -5A

Word problems, Mr.Carr is installing wall-to-wall carpeting in a room that ...

Mr.Carr is installing wall-to-wall carpeting in a room that measures 12 1/2ft. by 9ft. How much will it cost Mr. Carr if he purchases carpet priced at $26.00 per square yard?

Example of equations with radicals, Solve x =√(x+ 6) . Solution In ...

Solve x =√(x+ 6) . Solution In this equation the fundamental problem is the square root.  If it weren't there we could do the problem.  The whole procedure that we're going

Earthquake intensity, Earthquake Intensity Commonly the Richter scale i...

Earthquake Intensity Commonly the Richter scale is utilized to measure the intensity of an earthquake. There are several different ways of computing this depend on a variety of

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd