Intermediate Algebra – Student Workbook – Second Edition 2013

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

Lesson 6a - Exponents and Rational Functions Mini-Lesson Problem 5 MEDIA EXAMPLE – KEY CHARACTERISTICS OF RATIONAL FUNCTIONS a) Graph 4x f ( x) and determine the horizontal and vertical asymptotes and the domain. x 7 b) Graph 3x f ( x) and determine the horizontal and vertical asymptotes and the domain. 7 x 9 c) Quick Example: Find the Horizontal Asymptote for x 1 f ( x) . x 5 The ratio of highest degree terms in the numerator/denominator is y = x = 1 so the Horizontal x Asymptote for this function is y = 1. Scottsdale Community College Page 248 Intermediate Algebra
Lesson 6a - Exponents and Rational Functions Mini-Lesson SOLVE RATIONAL EQUATIONS BY GRAPHING To solve Rational Equations by graphing: Let y1 = one side of the equation Let y2 = other side of the equation Determine an appropriate window to see important parts of the graph Use the intersection method You may have more than one solution The x-value(s) of the intersection are your solutions Problem 6 WORKED EXAMPLE – SOLVE RATIONAL EQUATIONS BY GRAPHING Solve 3 5x 4 x 4 Let Y1 = 5x Let Y2 = 4 + 3/(x-4) Note use of ( ) Graph on window x: [-10..10], y:[-10..30] If you use standard window you do not see the upper intersection. You will need to perform the intersection process two separate times on your calculator. One time, you should get x = 0.62 (the left intersection) and the second time you should get x = 4.18. Be sure to move your cursor far enough (it has to go all the way across the vertical asymptote) to read the second intersection. Solutions, then, are x = 0.62, 4.18 Problem 7 MEDIA EXAMPLE – SOLVE RATIONAL EQUATIONS BY GRAPHING Solve 3x 3 1 by graphing. Round answer(s) to two decimals as needed. x 1 Scottsdale Community College Page 249 Intermediate Algebra
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Scottsdale Community College Interm
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Table of Contents Lesson 1a - Intro
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Lesson 1a - Introduction to Functio
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Lesson 1b - Linear Equations In the
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Lesson 1b - Linear Equations Mini-L
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Lesson 3a - Introduction to Exponen
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Lesson 4b - More on Logarithms This
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Lesson 4b - More on Logarithms Mini
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Intermediate Algebra – Student Workbook – Second Edition 2013

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