Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Accelerated Geometry B/Advanced Algebra Unit 7: Rational and Radical Relationships Excerpts from Georgia Department of Education Webinar September 19, 2013 [email protected] October 2013 Warm-Up If we raise both sides of an equation to a power, we sometimes obtain an equation which has more solutions than the original one. Which of the following equations result in extraneous solutions when you raise both sides to the indicated power? Explain. Which of the following equations result in extraneous solutions when you raise both sides to the indicated power? Explain. Solution: The square root symbol is defined to be the positive square root, so a positive root can never be equal to a negative number. [email protected] October 2013 What’s the main idea of Unit 7? • • • • • • Rewrite rational expressions Create equations that describe numbers or relationships Understand solving equations as a process of reasoning and explain the reasoning Represent and solve equations and inequalities graphically Interpret functions that arise in applications in terms of the context Analyze functions using different representations Concepts & Skills to Maintain from Previous Grades Computation with fractions Factoring polynomials Solving linear and quadratic equations laws of exponents, especially the power rule Websites to help with the above: http://www.crctlessons.com/ www.aplusmath.com www.aaamath.com Enduring Understandings from this Unit Recognize rational functions as the division of two polynomial functions and rewrite a rational expression Find the sum, difference, product, and quotient of rational expressions Graph rational and radical functions Interpret graphs and discover characteristics of rational functions Solve rational and radical equations algebraically and graphically Solve rational inequalities [email protected] October 2013 Examples & Explanations 1. The combined fuel economy (as defined by the federal Corporate Average Fuel Economy standard) for mpg in the city and mpg on the highway, is computed as: For most conventional cars, the highway fuel economy is 10 mpg higher than the city fuel economy. If the city fuel economy is Write your answer in the form of polynomials and the degree of mpg, what is the combined fuel economy in terms of where is less than the degree of , and ? are . Solution: So, y = x + 10 [email protected] October 2013 2. John makes DVDs of his friend’s shows. The cost of producing DVD is given by: Find an equation for the average cost per DVD and the domain of the average cost function. Solution: Domain: (Natural Numbers) Problem 3: The distance in miles ( your altitude in feet ( ) that you can see (toward the horizon) is dependent upon ), it is given by the formula (accounting for light refraction): Is it possible to see 200 miles to the horizon? Solution: One can see 200 miles to the horizon if they are approximately at an altitude of 23,000 ft. or just over 4 1/3 miles. (slightly below cruising altitude for airlines) [email protected] October 2013 The student edition for Unit 7 can be found at https://www.georgiastandards.org/Common-Core/Pages/Math-9-12.aspx On the left side, please look under mathematics, Accelerated Geometry B/Advanced Algebra. Then, the right side has a pull-down menu to access the units. Additional parent guides will be posted to the parent resource page on http://www.hallco.org/boe/index.php (right hand menu) as they become available. [email protected] October 2013