mac module 6

mac module 6 - MAC 1140 Module 6 Nonlinear Functions and...

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MAC 1140 Module 6 Nonlinear Functions and Equations II
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Rev.S08 2 Learning Objectives Upon completing this module, you should be able to 1. identify a rational function and state its domain. 2. find and interpret vertical asymptotes. 3. find and interpret horizontal asymptotes. 4. solve rational equations. 5. solve applications involving rational equations. 6. solve applications involving variations. 7. solve polynomial inequalities. 8. solve rational inequalities. http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.
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Rev.S08 3 Learning Objectives (Cont.) 9. learn properties of rational exponents. 10. learn radical notation. 11. use power functions to model data. 12. solve equations involving rational exponents. 13. solve equations involving radical expressions. http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.
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Rev.S08 4 Nonlinear Functions and Equations II http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. 4.5 4.5 Rational Functions and Models Rational Functions and Models 4.6 4.6 Polynomial and Rational Inequalities Polynomial and Rational Inequalities 4.7 4.7 Power Functions and Radical Equations Power Functions and Radical Equations There are three sections in this module:
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Rev.S08 5 What is a Rational Function? A rational function is a nonlinear function. The domain of a rational function includes all real numbers except the zeros of the denominator q(x). http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.
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Rev.S08 6 What is a Vertical Asymptote? http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. In this graph, the line x = 2 is a vertical asymptote .
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Rev.S08 7 What is a Horizontal Asymptote? http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. In this graph, the line y = 25 is a horizontal asymptote .
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Rev.S08 8 Let’s Look at an Example http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. Use the graph of to sketch the graph of Include all asymptotes in your graph. Write g ( x ) in terms of f ( x ). Solution g ( x ) is a translation of f ( x ) left one unit and down 2 units . The vertical asymptote is x = 1 The horizontal asymptote is y = 2 g ( x ) = f ( x + 1) 2 2 1 ( ) f x x = 2 1 ( ) 2. ( 1) g x x = ! +
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Rev.S08 9 How to Find Vertical and Horizontal Asymptotes? http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.
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Rev.S08 10 More Examples http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. For each rational function , determine any horizontal or vertical asymptotes. a) b) c) Solution To identify horizontal asymptote, look at the leading coefficient of the highest power term in both numerator and denominator. a) Horizontal Asymptote : If the Degree of numerator equals the degree of the denominator, y = a/b is asymptote, so y = 2/4 = 1/2 To identify vertical asymptote, set the denominator to 0.
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mac module 6 - MAC 1140 Module 6 Nonlinear Functions and...

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