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# Class Note for MATH 1310 at UH 3

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This 10 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 16 views.

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Date Created: 02/06/15

A function ofthe form Px anx 61le 612x2 alx do Where an i 0 and the exponents on x are Whole numbers is called a polynomial function of degree n The number an is called the leading coefficient and the term anx quot is called the leading term The number aois called the constant term Graph Properties of Polynomial Functions Let P be an nthdegree polynomial function with real coefficients P is continuous for all real numbers The graph of P is a smooth curve The graph of P has at most 11 xintercepts 759 The graph of P has at most 11 l turning points Example 1 Given the following polynomial function state the leading term the degree of the polynomial and the leading coefficient Px 5x3 2x 1 Example 2 Given the following polynomial function state the leading term the degree of the polynomial and the leading coefficient Px 2x 12x37 End Behavior of Polynomial Functions The behavior of a graph of a function to the far left or far right is called its end behavior The end behavior of a polynomial function is revealed by the leading term of the polynomial function Zeros of Polynomial Functions If f is a polynomial function the values of x for which fx is equal to 0 are called the zeros off Example 3 Given the following polynomial function find the zeros Px xx 125x 35 Example 4 Given the following polynomial function find the zeros Px x3 x2 2x Multiplicity of a Zero In factoring the equation for the polynomial function f if the same factor x i r occurs k times we call r a repeated zero with multiplicity k Example 5 Given Px 3x8 x 23 5x D6 the multiplicity of the zero 0 is 2is is Steps in Graphing Other Polynomials 1 Determine the leading term its degree and the sign of the leading coefficient 2 Determine the end behavior The end behavior will look like the end behavior of one of the following fx fx x2 fx or fx x3 3 Factor the polynomial function if necessary Make a table listing the factors zeros multiplicities and describe the behavior at each xintercept Description of the behavior at each zero xintercept Even Multiplicity The graph touches the xaXis but does not cross it and it looks like a parabola there Odd Multiplicity 0f 1 The graph crosses the xaXis and it looks like a line there Odd Multiplicity gt 1 The graph crosses the xaXis and it looks like a cubic there 4 Find the yintercept 5 Draw the graph being careful to make a nice smooth curve with no sharp corners Note Without calculus or plotting lots of points we don t have enough information to know how high or how low the turning points go Example 6 Sketch the graph of the function P x x 22 x 1 Example 7 Sketch the graph of the function Px x 2x 16 x 15 Example 8 Sketch the graph of the function Px x5 4 x3 Example 9 Sketch the graph of the function Px x4 x3 6x2 Math 13 10 Chapter 4 Section 41 Polynomial Functions

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