Polynomial Functions, Study notes of Mathematics

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OM DUG Polynomial Functions | 2G nots. In the previous unit we discussed polynomial functions in terms of finding their zeros. A polynomial function of degree n can be written in the form S(x)=a,x" tax" bet age +axt ay, where d,,4, )..+.4;,4,.4, are real numbers and a, #0. [The reason we use the subscripts for the coefficient values is because there is no limit to how many terms we can have in a polynomial function. For a quadratic equation we could simply use a, 6, and ¢ because there are at most three terms. The form above is meant to work for all polynomial functions. But there is no need to get hung up on the notation] Oftentimes we see polynomial functions written in a form that is very similar to the other nonlinear functions we discussed in the previous unit. S(x)=a(x—-A) +k Functions with an even degree will have shapes that are similar to a parabola, and functions with an odd degree have the “cactus” shape of the cubing function. Here is a chart that describes the end behavior of polynomial functions based on their degree and leading coefficient: a>0 a<0 NAIL N as xX —-—29 asx as x —+—0 asx nis odd nis even J T* f \ as x —>—<20 asx | asx—»—0 as x90