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Alg II Chapter 8 Part 1 Notes.notebook
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February 12, 2015
Algebra IIChapter 8 Part 1: Rational Functions
Vocabulary
Chapter 8 Lesson 1Model Inverse and Joint Variation
Note:
Direct Variation is in the form of y=ax!
Alg II Chapter 8 Part 1 Notes.notebook
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Example 1: Classify Direct and Inverse Variation
Example 2: Write an Inverse Variation Equation Writing an Inverse Variation Equation:1. Substitute x and y into y=a/x.2. Solve for a.3. Rewrite y=a/x using the new a value.
Alg II Chapter 8 Part 1 Notes.notebook
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Example 3:Write and Inverse Variation Model
Example 4: Check Data for Inverse Variation
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Example 5: Write a Joint Variation Equation
Writing a Joint Variation Equation:1. Write the relationship using variables. 2. Substitute all possible variables.3. Solve for a.4. Rewrite the relationship using the new a value.
Example 6: Compare Different Types of Variation
Alg II Chapter 8 Part 1 Notes.notebook
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Chapter 8 Lesson 2Graph Simple Rational Functions
VocabularyWords to Review:
DomainRangeAsymptote
Figuring Out Vertical Asymptotes
Ex:
Vertical Asymptote: x = 5 and x = 4
Ex:
Vertical Asymptote: x = 2
Ex:
Vertical Asymptote: x = 0
To find Vertical Asymptotes, set the denominator equal to zero and solve. (Note: This is where the function is "undefined" because you would be dividing by zero!"
Work:
Work:
Work:
Alg II Chapter 8 Part 1 Notes.notebook
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B igger (Exponent)O nB ottomO (zero)
B igger (Exponent) O nT opN one
E xponents A reT heS ame
D ivideC oefficients
Figuring Out Horizontal Asymptotes
Ex:
Horizontal Asymptote: y = 0
Ex:
Horizontal Asymptote: none
Ex:
Horizontal Asymptote: y = 2
Use BOBO BOTN EATS DC to help you remember how to find the horizontal asymptotes.
Example 1: Graph a Rational Function of the Form
Graphing Rational Equation in y=a/x form:1. Find and draw the asymptotes.
Vertical: Set denominator equal to zero and solve.Horizontal: BOBO BOTN EATS DC
2. Make a table of values.3. Plot several points to the left and right of the
vertical asymptote. 4. Draw the branches of the hyperbola.
State any asymptotes.
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Example 3: Graph a Rational Function of the Form Graphing Rational Equation in form:
1. Find and draw the asymptotes. *Vertical: Set denominator equal to zero and solve.
*Horizontal: BOBO BOTN EATS DC2. Make a table of values.3. Plot several points to the left and right
of the vertical asymptote. 4. Draw the branches of the hyperbola.
Example 4: Solve a MultiStep Problem
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Example 2: Graph a Rational Function of the Form
Graphing Rational Equation in y=a/x form:1. Find and draw the asymptotes.
Vertical: Set denominator equal to zero and solve.Horizontal: BOBO BOTN EATS DCNote: Be careful! K values shift the horizontal asymptote!!!
2. Make a table of values.3. Plot several points to the left and right of the
vertical asymptote. 4. Draw the branches of the hyperbola.
State any asymptotes.
Chapter 8 Lesson 3Graph General Rational FunctionsVocabulary
Words to Review:End BehaviorAsymptoteRational Function
Note:*m is the degree of the numerator*n is the degree of the denominator
This chart simply describes BOBO BOTN EATS DC in math terminology.
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Example 1: Graph a Rational Function (m<n) Note:*To find the xintercepts you can find the zeroes of the polynomial in the numerator!*Set the numerator equal to zero and solve!
Identify any xintercepts and asymptotes.
Note:*To find the vertical asymptotes, set the denominator equal to zero and solve!*To find the horizontal asymptotes, BOBO BOTN EATS DC.
Example 2: Graph a Rational Function (m=n) Note:*To find the xintercepts you can find the zeroes of the polynomial in the numerator!*Set the numerator equal to zero and solve!
Note:*To find the vertical asymptotes, set the denominator equal to zero and solve!*To find the horizontal asymptotes, BOBO BOTN EATS DC.
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Example 3: Graph a Rational Function (m>n) Note:*To find the xintercepts you can find the zeroes of the polynomial in the numerator!*Set the numerator equal to zero and solve!
Note:*To find the vertical asymptotes, set the denominator equal to zero and solve!*To find the horizontal asymptotes, BOBO BOTN EATS DC.
Example 4: Solve a MultiStep Problem