trouble with graphs of polynomials.

so im having trouble understanding the concept of assuming the graphs of polynomials. i wish i had exmaple questions but i dont, so i thought someone here could help.

things i dont understand:

- how to tell the least degree of a polynomial function.( i originally thought that it was by how many roots there were but doesnt seem to work for me.)

- how to tell whether the leading coefficient is positive or negative.

any help is appreciated. thanks

Re: trouble with graphs of polynomials.

Re: trouble with graphs of polynomials.

I am not sure there is a universally accepted concept of "the least degree" of a polynomial. The degree of a polynomial is the highest degree of its terms, where the degree of a term is . Thus, the degree of is .

It's difficult to determine the degree from a graph when the axes are not graduated. For example, the graphs of and look similar. The number of real roots of a polynomial does not exceed its degree, but it can be strictly less than the degree.

For any polynomial , as . You can tell whether the degree of is even or odd by observing the behavior at ±∞: if tends to infinities of the same sign when x tends to +∞ and -∞, then the degree is even; if, for example, as and as , then the degree is odd.

The leading coefficient of is positive iff as , and it is negative iff as .

Re: trouble with graphs of polynomials.

@topsquark,

i understand how to find those things while seeing the polynomial infront of me the problem is interpreting that infromation from a graph.

for the polynomial you gave me the least degree would be 1, and the leading coefficient would be -8.

@emakarov i think im starting to understand now, thanks i will continue to use your post as a reference as i study for my finals