The document provides an overview of polynomial functions, including their definition, degree, and methods for graphing and analyzing them. It includes various examples, solutions, theorems, and visual aids such as figures and tables to help illustrate concepts. Additionally, it covers real zeros of polynomial functions, their multiplicity, and how to build cubic models from data.

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Chapter 4
Section 1

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Identify Polynomial
Functions and Their
Degree

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Definition

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Example

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Example 1 Solution

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Table

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Figure

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Definition

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Figure

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Table

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Figure

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Figure

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Figure

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Figure

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Graph Polynomial
Functions Using
Transformations

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Figure: Graph of f(x) = 1 – x5

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Example

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Solution
Figure 8

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Identify the Real
Zeros of a
Polynomial Function
and Their Multiplicity

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Graph of a Polynomial Function

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Definition

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The following statements are equivalent:

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Figure: f(x) = x3
- 4x2
- 11x + 30

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Definition

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Example

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Solution

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Solution continued

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Table 3

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Figure 11

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Theorem

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Figure:
2
1 ( 1) ( 2)
Y x x
  

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Example
Figure 13

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Solution

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Theorem

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f(x)= -2x3
+ 5x2
+ x - 4

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Figure: End behavior

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Example
Figure 16

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Solution

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Example 9
Figure 17

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Solution

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Analyze the Graph of
a Polynomial
Function

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Example

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Solution

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Solution continued

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Solution continued

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Solution continued

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Solution continued

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Solution continued

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Figure
3 2
( ) 2.48 4.3155 2.484406
f x x x
   

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Table
Points on either side of the x-intercept.

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Figure: 3 2
( ) 2.48 4.3155 2.484406
f x x x
   

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Build Cubic Models
from Data

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Figure: Cubic relation

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Table

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Figure

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Figure

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Figure