Polynomial FunctionsChapter 6

Section 6.4Polynomial Functions

By the end of this section, you will be able to:

1. Evaluate polynomial functions;

2. Identify general shapes of graphs od polynomial functions.

Class notes from Monday 2/10/14

Assignment Due Tuesday, 2/11/14:

A# 6.4: Page 336 #12 – 32 even

Polynomial Functions

What patterns do you see in a honeycomb?

𝑓 (𝑟 )=3𝑟2−3𝑟+1

𝑟=¿¿

𝑓 (𝑟 )=¿¿VOCAB: Polynomial in one variable

3 𝑥5+2𝑥4−5 𝑥3+𝑥2+1

Polynomial In One Variable

Degree of a polynomial in one variable: _________________________________________

Leading Coefficient: _________________________________________________________

Polynomial In One Variable

Polynomial ExpressionDegre

e

Leading Coefficie

nt

Example 1: Find Degrees and Leading Coefficients

Polynomial in one variable?

Degree =

Leading coefficient =

Polynomial in one variable?

Degree =

Leading coefficient =

Example 2: Evaluating Polynomial Functions

Find the total number of hexagons in a honeycomb with 12 rings.

Find the total number of hexagons in a honeycomb with 20 rings.

Example 3: Function Values of Variables

Find Find

PRACTICE Example 3: Function Values of Variables

1. 2.

Graphs of Polynomial Functions

End Behavior…..Even Functions

Degree: Even

Leading Coefficient:____________________

End Behavior:

Degree: Even

Leading Coefficient:____________________

End Behavior:

Domain: __________________

Range: ____________________

Domain: __________________

Range: ____________________

End Behavior…..Odd Functions

Degree: Odd

Leading Coefficient:____________________

End Behavior:

Degree: Odd

Leading Coefficient:____________________

End Behavior:

Domain: __________________

Range: ____________________

Domain: __________________

Range: ____________________

Example 4: Graphs of Polynomial FunctionsFor each graph:a. Describe the end behaviorb. Determine whether it represents an odd-degree or even-degree polynomial functionc. State the number of real zeros