Algebra 2B Chapter 9

Lesson 9.1 Learning Targets: I can simplify Rational Expressions I can simplify complex fractions

Vocabulary Rational 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 Techniques For 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: x 2 − y 2 = ( x + y) ( x − y) b.difference of cubes: x 3 − y 3 = ( x − y) ( x 2 + xy + y 2 ) c.sum of cubes: x 3 + y 3 = ( x + y) ( x 2 − xy + y 2 ) For a trinomial, use the T ax 2 + bx + c:

Step1: Factor the numerator and denominator completely Step 2: Reduce any common factors 2 Step 3: Simplify

Step1: Factor the numerator and denominator completely Step 2: Reduce any common factors 2 Step 3: Simplify

Step1: Make into a multiplication problem Step2: Factor the numerator and denominator completely Step 3: Reduce any common factors Step 4: Simplify

Step1: Make into a multiplication problem Step2: Factor the numerator and denominator completely 3 Step 3: Reduce any common factors 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:

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

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): _____________________________

xf(x) Asymptote(s): ________________________ Hole(s): _____________________________

xf(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: _________________ Simplify:

Warm-up 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:

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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