Leading coefficient test, Algebra

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.

Posted Date: 4/8/2013 2:48:10 AM | Location : United States







Related Discussions:- Leading coefficient test, Assignment Help, Ask Question on Leading coefficient test, Get Answer, Expert's Help, Leading coefficient test Discussions

Write discussion on Leading coefficient test
Your posts are moderated
Related Questions
i need to know the steps to 3x+4y=8 and -5x-3y=5 using the substitution method.

9-4x, for x=5 what is the answer

17b-29=39


Find regular grammar for a(a+b)*(ab*+ba*)b

1.(x+y+1)² 2.(x+y-1)² 3.(x-y-1)² 4.(-x-y-1)² question: what is the effect of switching the plus sign to minus sign on the product

Working together Jack and Bob can clean a place in 30 minutes. On his own, Jack can clean this place in 50 minutes. How long does it take Bob to clean the same place on his own?


Here are two one-to-one functions f (x ) and g ( x ) if     (f o g )( x ) = x           AND                         ( g o f ) ( x ) = x then we say that f ( x )& g ( x ) are

25 equations that equall 36