Download Parent Unit 3 Guide for Advanced Algebra

Accelerated Geometry B/Advanced
Algebra
Unit 7: Rational and Radical
Relationships
Excerpts from Georgia Department of
Education Webinar September 19, 2013
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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.
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October 2013
What’s the main idea of Unit 7?
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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
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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
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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
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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
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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)
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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.
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October 2013