Algebra 2B

Chapter 9

Lesson 9.1

Learning Targets:

• I can simplify Rational Expressions

• I can simplify complex fractions

VocabularyRational Expression: It’s the ratio of two polynomial expressions

Examples:

Complex Fraction: It’s a rational expression whose numerator and/or denominator contains a rational expression.

Examples:

Multiplying Rational Expressions:

Dividing Rational Expressions:

Review:How to multiply and divide monomials:

How to multiply, divide and find the power of a power:

How to factor polynomials:

Summary of Factoring TechniquesFor all polynomials, first factor out the greatest common factor (GCF).For a binomial, check to see if it is any of the following:

a.difference of squares: x2 − y2 = ( x + y) ( x − y) b.difference of cubes: x3 − y3 = ( x − y) ( x2 + xy + y2) c.sum of cubes: x3 + y3 = ( x + y) ( x2 − xy + y2)

For a trinomial, use the Tax2 + bx + c:

Step1: Factor the numeratorand denominator completely

Step 2: Reduce any commonfactors2

Step 3: Simplify

Step1: Factor the numeratorand denominator completely

Step 2: Reduce any commonfactors2

Step 3: Simplify

Step1: Make into amultiplication problem

Step2: Factor the numeratorand denominator completely

Step 3: Reduce any commonfactors

Step 4: Simplify

Step1: Make into amultiplication problem

Step2: Factor the numeratorand denominator completely

3Step 3: Reduce any commonfactors

Step 4: Simplify

2 2

Continue factoring!!!

Closure 9.1(in class):

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Lesson 9.2

Learning Targets :

• I can determine the LCM of polynomials

• I can add and subtract rational expressions

Vocabulary To add and subtract Rational Expressions:

To find equivalent fractions with the same denominator, we need the LCM.

Your Turn:

Your Turn:

Your Turn:

Your Turn:

Closure Lesson 9.2 (in class):

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Lesson 9.6

Learning Targets :

I can solve Rational Equations

Vocabulary

A rational equation is ____________________________________________

____________________________________________________________

Hint: When solving a rational equation, eliminate the fractions first!

Check the solutions in the original equation

Warm-up 9.3

4.

5.

Lesson 9.3

Learning Targets :

• I can determine the Vertical Asymptotes and the Point of Discontinuity (Hole)

• I can graph Rational Functions

Vocabulary

Continuity:_________________________________________________

_________________________________________________________

To find the asymptote(s) and/or hole(s) of a rational function, we look at its denominator.

Asymptote(s): ________________________

Hole(s): _____________________________

In your own words,

vertical asymptote: _______________________________________________ _______________________________________________

hole: _______________________________________________ _______________________________________________

x

f(x)

Asymptote(s): ________________________

Hole(s): _____________________________

x f(x)

Asymptote(s): ________________________Hole(s): _____________________________

x f(x)

Asymptote(s): ________________________Hole(s): _____________________________

Use your graphing calculator to get the table of values.

Asymptote(s): ________________________Hole(s): _____________________________

Asymptote(s): ________________ Asymptote(s): _______________Hole(s): _____________________ Hole(s): ____________________

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Warm-up 9.4: on the back of closure

Asymptote: ____________

Hole: _________________

Asymptote: ____________

Hole: _________________

3.

4.

Simplify:

Warm-up 9.4

3.

4.

Simplify:

Lesson 9.4

Learning Targets :

• I can recognize and solve direct and joint variation problems

• I can recognize and solve inverse variation problems

Vocabulary

Examples:

Examples:

Closure Lesson 9.4 (in class):

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Lesson 9.5

Learning Targets :

• I can identify graphs as different types of functions

• I can identify equations as different types of functions

Use your Family Functions Cheat sheet to identify the functions represented by each graph.

________________________ __________________________

______________________ _______________________

_______________________ _________________________

________________________ __________________________

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Today, you must do in class:

1. Study guide & Review

2. Practice test (Multiple choice)

Homework:

Practice test from book (worksheet available)

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