when presented with the graph of a polynomial function, there are several pieces of information we can get from the graph of the polynomial, without ever actually seeing the equation.First, though, we must establish some terminology. When given a polynomial in the form:
, ,We refer to the degree of the polynomial as n, because n is the highest non-zero power of x in the polynomial. We need to be clear that all exponents on the variable x must be nonnegative integers in order for f(x) above to be a polynomial. We call the leading coefficient, since it accompanies the x with the highest power. For example, in the polynomial , the degree is 4, and the leading coefficient is -13.The first piece of information we can extract is whether the degree of a polynomial is odd or even. In order to do this, we look at both “sides” of the graph: if they both go up or both go down, the degree is even. If they go opposite directions, that is, one goes up and one goes down, then the degree is odd.
