algebra 2b chapter 9. lesson 9.1 learning targets: i can simplify rational expressions i can...
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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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