1310-Notes-Sec-41-filled

1310-Notes-Sec-41-filled - Math 1310 Section 4.1 Polynomial...

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Math 1310 Class Notes – Section 4.1, Page 1 of 10 Math 1310 Section 4.1 Polynomial Functions General information A polynomial function is a function of the form 0 1 2 2 2 2 1 1 ) ( a x a x a x a x a x a x P n n n n n n + + + + + + = - - - - where 0 n a , n a a a , , , 1 0 are real numbers and n is a whole number. The degree of the polynomial function is n . We call the term n n x a the leading term, and n a is called the leading coefficient. . ) 0 ( 0 a P = Our objectives in working with polynomial functions will be, first, to gather information about the graph of the function and, second, to use that information to generate a reasonably good graph without plotting a lot of points. In later examples, we’ll use information given to us about the graph of a function to write its equation. Power functions We’ll start with the shapes of the graphs of functions of the form . 0 , ) ( = n x x f n You should be familiar with the graphs of 2 ) ( x x f = and . ) ( 3 x x g =
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Math 1310 Class Notes – Section 4.1, Page 2 of 10 The graph of 0 , ) ( = n x x f n , n is even, will resemble the graph of 2 ) ( x x f = , and the graph of 0 , ) ( = n x x f n , n is odd, will resemble the graph of 3 ) ( x x f = .
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Math 1310 Class Notes – Section 4.1, Page 3 of 10 End behavior Next, you will need to be able to describe the end behavior of a function. If the degree of the function is even and
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1310-Notes-Sec-41-filled - Math 1310 Section 4.1 Polynomial...

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