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Chapter Planner

Power, Polynomial, and Rational FunctionsPower, Polynomial, and Rational Functions

84A | Chapter 2 | Power, Polynomial, and Rational Functions

All digital assets are Interactive Whiteboard ready.Diagnostic Assessment

Quick Check, p. 85

Pacing: 2 days

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Title

Power and Radical

FunctionsGraphing Technology Lab: Behavior of GraphsPolynomial FunctionsGraphing Technology Lab: Hidden Behavior of Graphs

Objectives

Graph and analyze power

functions.

Graph and analyze radical

functions and solve radical equations.

Graph and analyze the

behavior of polynomial functions.

Graph polynomial functions.

Model real-world data with

polynomial functions.

Use TI-Nspire to explore the

hidden behavior of graphs.

Key Vocabulary

power function, monomial function, radical function,

extraneous solutionspolynomial function, leading coefficient, leading-term test, turning point, quadratic form, repeated zero, multiplicity

NCTM Standards

2, 3, 6, 7, 8, 9, 1032, 3, 4, 6, 7, 8, 9, 103

Multiple

Representations

p. 94p. 106

Lesson Resources

connectED.mcgraw-hill.com Worksheets

Vocabulary

Personal Tutor Self-Check Quiz

5-Minute Check

Study Notebook

connectED.mcgraw-hill.com

TI-83/84 Plus or other

graphing calculator connectED.mcgraw-hill.com Worksheets

Vocabulary Animations

Personal Tutor

Self-Check Quiz

5-Minute Check

Study Notebook

connectED.mcgraw-hill.com

TI-Nspire technology

Resources for Every

Lesson eStudent Edition

eTeacher Edition

Interactive Classroom

Assessment

Differentiated

Instruction

pp. 90, 91, 95pp. 100, 107

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Suggested Pacing

Time Periods Instruction Review & Assess Total

45-minute 13 days 2 days 15 days

90-minute 6 days 1 day 7 days

Pacing:

2 days

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The Remainder and Factor

TheoremsZeros of Polynomial Functions Rational FunctionsNonlinear Inequalities

Divide polynomials using long division

and synthetic division.

Use the Remainder and Factor

Theorems.

Find real zeros of polynomial functions.

Find complex zeros of polynomial

functions.

Analyze and graph rational functions.

Solve rational equations.

Solve polynomial inequalities.

Solve rational inequalities.

synthetic division, depressed polynomial, synthetic substitution

Rational Zero Theorem, Descartes Rule

of Signs, Fundamental Theorem of

Algebra, Linear Factorization Theorem,

complex conjugatesrational function, asymptote, vertical asymptote, horizontal asymptote, oblique asymptote, holes

polynomial inequality, sign chart, rational inequality

2, 6, 7, 8, 9, 102, 3, 6, 7, 8, 9, 102, 3, 6, 7, 8, 9, 102, 6, 7, 8, 9, 10

p. 116p. 128p. 139p. 146 connectED.mcgraw-hill.com

Worksheets

Vocabulary

Personal Tutor

Virtual Manipulatives

Self-Check Quiz

5-Minute Check

Study Notebook

connectED.mcgraw-hill.com

Worksheets

Vocabulary

Animations

Personal Tutor

Virtual Manipulatives

Self-Check Quiz

5-Minute Check

Study Notebook

connectED.mcgraw-hill.com

Worksheets

Vocabulary

Personal Tutor

Self-Check Quiz

5-Minute Check

Study Notebook

connectED.mcgraw-hill.com

Worksheets

Vocabulary

Personal Tutor

Self-Check Quiz

5-Minute Check

Study Notebook

eStudent Edition eTeacher Edition

Interactive Classroom

Assessment

pp. 110, 117pp. 124, 129pp. 132, 136pp. 143, 144

Formative Assessment

Mid-Chapter Quiz, p. 118

Study Guide and Review, pp. 148...152

Practice Test, p. 153

Connect to AP Calculus pp. 154...155

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SE = Student Edition, TE = Teacher Edition, CRM = Chapter Resource Masters

Assessment and Intervention

84C | Chapter 2 | Power, Polynomial, and Rational Functions

2 A Power, Polynomial, and Rational FunctionsPower, Polynomial, and Rational Functions

DiagnosisPrescription

DIAGNOSTICASSESSMENT

Beginning Chapter 2

Get Ready for the Chapter SEResponse to Intervention TE

Beginning Every Lesson

Then, Now, Why? SE

5-Minute Check

During/After Every Lesson

FORMATIVEASSESSMENT

Guided Practice SE, every example

H.O.T. Problems SE

Spiral Review SE

Additional Examples TE

Watch Out! TE

Step 4, Assess TE

Self-Check Quizzes

connectED.mcgraw-hill.comTIER 1 InterventionPractice CRM connectED.mcgraw-hill.com

TIER 2

InterventionDifferentiated Instruction TE;

Study Guide and Intervention Masters CRM

Mid-Chapter

Mid-Chapter Quiz SE

AssessmentTIER 1 Intervention Practice CRM

connectED.mcgraw-hill.com

TIER 2

Intervention Differentiated Instruction TE;

Study Guide and Intervention Masters CRM

Before Chapter Test

Chapter Study Guide and Review SE

Practice Test SE

Chapter Test

connectED.mcgraw-hill.com

Vocabulary Review connectED.mcgraw-hill.com

AssessmentTIER 1 Intervention Practice CRM

connectED.mcgraw-hill.com

TIER 2

Intervention Differentiated Instruction TE;

Study Guide and Intervention Masters CRM

After Chapter 2

SUMMATIVEASSESSMENT

Multiple-Choice Tests CRM

Free-Response Tests CRM

Vocabulary Test CRM

Extended Response Test CRM

AssessmentStudy Guide and Intervention CRM

connectED.mcgraw-hill.com

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Differentiated Instruction

2 D Power, Polynomial, and Rational FunctionsPower, Polynomial, and Rational Functions

Option 1 Reaching All Learners

ALOL BLELL Logical Learners Have groups of students write and graph six functions, two for each of the following types: f (x ) =x n , f (x ) =x n , and f (x ) =x p _ n , where n and p are positive integers and p _ n is in simplest form. Have students write each function and each graph on a separate index card. Groups trade cards and try to match each graph with its function. = g x()x 4 y x O Visual/Spatial Learners Have students use grid paper and colored pencils to help organize their work when performing synthetic division. For example, have students write 6 x 3 - 25 x 2 18 x + 9 divided by x - 3 with color as shown. Then have them write on grid paper with the same colors. 36

6-25 18 9

18-21-9

7-30

Option 2 Approaching Level

AL Divide students into groups of three or four. Have students take turns explaining how to determine the end behavior of the graph of a polynomial function and how to locate the zeros of the function. Have them describe how knowing this information helps them graph the polynomial.

Option 3 English Learners

ELL Provide students with a photocopy of some or all of the word problems from this chapter. Before they begin to solve the problems, have students highlight all words they do not understand. Pair each ELL student with a partner with fluent English-language skills and have them discuss the meanings of the highlighted words.

Option 4 Beyond Level

BL Have students take a picture of a nonlinear item. Ask them to superimpose a coordinate grid and sketch a curve over a section of the picture as shown. Then have students locate points on the graph and use those points and the CubicReg tool on their calculators to write a polynomial function that models that portion of the curve. The example below is a close-up of a zebras pattern. The function f (x ) = 0.011 x 3 - 0.217 x 2 + 1.359 x + 0.234 comes close to this portion of the pattern. x y

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Focus on Mathematical Content

Power, Polynomial, and Rational FunctionsPower, Polynomial, and Rational Functions

84E | Chapter 2 | Power, Polynomial, and Rational Functions

Lesson-by-Lesson PreviewVertical Alignment

2-1 Power and Radical Functions

Functions of the form

f (x ) = a x n , where a and n are constant real numbers, are power functions. A power function is also a type of monomial function. A monomial function is any function that can be written as f (x ) = a or f (x ) = a x n , where a and n are nonzero constant real numbers. If n is an even positive integer: y x

Even Degree

If n is an odd positive integer: y x

Odd Degree

Power functions of the form

f (x ) = x p _ n can be written as radical functions of the form f (x ) = n x p , where n and p are positive integers greater than 1 that have no common factors. Note that the domain may be restricted to nonnegative values. If n is an even positive integer: y x

Even Degree

If n is an odd positive integer: y x

Odd Degree

Before Chapter 2

quotesdbs_dbs12.pdfusesText_18

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