Mathematical Analysis (Honors)
Unit 6: Radical and Special Functions
Students build on their work with quadratic and absolute value functions and extend their repertoire of functions to begin to explore other function families. Students discover the connections between changes in algebraic equations and transformations in the corresponding graphs. Students compare properties of two functions using multiple representations, such as, a graph, table of values, and verbal descriptions. Students begin to fit realworld data and scenarios to potential function families. This unit serves as an introduction to function families, transformations, and modeling and lays the groundwork for deeper study of individual function families.
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Students will:
Extend the properties of exponents to rational exponents.
N.RN.A.2
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Model relationships between two quantities with functions in order to solve realworld problems.
MA.RSF.A.1
Determine the domain, range, and end behavior of radical functions.
MA.RSF.A.2
Use graphical and algebraic methods to solve radical equations and inequalities.
MA.RSF.A.3
Sketch and analyze the graphs of absolute value, greatest integer, and piecewise functions.
MA.RSF.A.4
Model realworld problems with radical and special functions, identifying necessary restrictions on the model.
MA.RSF.A.5
Use radical functions to model and solve realworld problems.
MA.RSF.A.6
Solve inequalities involving absolute value functions.
Extend the properties of exponents to rational exponents.
N.RN.A.2
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
 Background Info.
 Check for Understanding: Simplifying Rational Exponent Expressions
 Review/Rewind: Simplifying Mixed Radical and Rational Expressions
 Enrichment Tasks: Extending the Definition of Exponents, Variation 2
Model relationships between two quantities with functions in order to solve realworld problems.
MA.RSF.A.1
Determine the domain, range, and end behavior of radical functions.
 Background Info.
 Check for Understanding: Determine the domain of Functions
 Review/Rewind: Domain of a Radical Function
 Enrichment Tasks: Determine the Domain of Functions
MA.RSF.A.2
Use graphical and algebraic methods to solve radical equations and inequalities.
 Background Info.
 Check for Understanding: Solving Square Root Equations
 Review/Rewind: Solving Square Roots(1)  Solving Square Roots(2)  Solving Square Roots(3)  Solving Cubed Roots
 Enrichment Tasks: Radical Equations
MA.RSF.A.3
Sketch and analyze the graphs of absolute value, greatest integer, and piecewise functions.
 Background Info.
 Check for Understanding: Evaluating Piecewise Functions From the formula  Evaluating Step Functions from their Graph
 Review/Rewind: Piecewise Functions
 Enrichment Tasks: Piecewise Functions
MA.RSF.A.4
Model realworld problems with radical and special functions, identifying necessary restrictions on the model.
MA.RSF.A.5
Use radical functions to model and solve realworld problems.
 Enrichment Tasks: Who Wins the race?
MA.RSF.A.6
Solve inequalities involving absolute value functions.
 Background Info.
 Check for Understanding:
 Review/Rewind: Solving Absolute Value Inequalities
What are some signs of student mastery?

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