Analyzing and Graphing Radical Functions, Study notes of English

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Unit 8: Radical &

Rational Functions

LG 8-1 Radical Functions

LG 8-2 Rational Functions

TEST 5/22 – the last day of school!

remediation

LG 8-1 Radical Functions

1. We will SOLVE them! Understand solving equations as a process of reasoning and explain the reasoning

• (^) MGSE9-12.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

2. We will GRAPH them! Analyze functions using different representations

• MGSE9-12.F.IF.7 Graph square root, cube root functions expressed algebraically and show key features of the graph both by hand and by using technology.
• (^) MGSE9-12.F.IF.4 Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior;

3. We will ANALYZE them! Create equations that describe numbers or relationships

• (^) MGSE9-12.A.CED.2 Create radical functions in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret functions that arise in applications in terms of the context
• MGSE9-12.F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

SELECTED TERMS AND SYMBOLS

• (^) Extraneous Solutions: A solution of the simplified form of

the equation that does not satisfy the original equation.

• (^) Inequality : Any mathematical sentence that contains the

symbols > (greater than), < (less than), < (less than or equal

to), or > (greater than or equal to).

EVIDENCE OF LEARNING By the conclusion of this unit, you should be able to demonstrate the following competencies:

• (^) Solve radical equations
• (^) Graph radical functions and identify key characteristics
• (^) Interpret solutions to graphs and equations given the context of the problem

Example 1: Solving Equations Containing One Radical

Example 2: Solving Equations Containing One Radical

Extraneous Solutions

• (^) Raising each side of an equation to an even power

may introduce extraneous solutions.

• (^) You don’t have to worry about extraneous solutions

when solving problems to an odd power.

Example 9: Solving Equations with Rational Exponents 2 x = (4 x + 8) 1 2

Example 10 3( x + 6) = 9 1 2

• You Try! Example
• Example
• You Try! Example
• Example
• Class work/Homework: Page 462 #1 –
• Warm Up 5/