Algebra 1 (& GT)
Unit 5: Modeling with Other Functions
As an extension of their work with various function families, students will begin to investigate the graphs of simple nonlinear functions. Students will explore the graphical representations of other models, to include square root, cube root, and piecewisedefined functions, including step functions and absolute value functions. Students will be able to graph these functions by hand in simple cases and by using technology in more complex cases. In all cases, students should identify key features of their graphs. Students should identify parent functions and describe or sketch the effects of simple transformations on those parent functions.
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What will my child learn?
Students will:
Analyze functions using different representations.
F.IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
b. Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions.
Extend the properties of exponents to rational exponents.
N.RN.A.1
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^1/3 to be the cube root of 5 because we want (5^1/3)^3 = 5^(1/3)3 to hold so (5^1/3)^3 must equal 5 (SAT® Content  PAM.06).
N.RN.A.2
Rewrite expressions involving radicals and rational exponents using the properties of exponents (SAT® Content  PAM.06).
Students will:
Analyze functions using different representations.
F.IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
b. Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions.
 Background Info.: Graphs of Absolute Value Functions*  Finding a Piecewise Function from a Graph*  Graphs of Absolute Value Functions*
 Check for Understanding: Graphs of Absolute Value Functions  Graphs of Piecewise Linear Functions
 Review/Rewind: Introduction to Graphs of Absolute Value Functions  Introduction to Piecewise Functions
 Enrichment Task: Bank Account Balance
Extend the properties of exponents to rational exponents.
N.RN.A.1
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^1/3 to be the cube root of 5 because we want (5^1/3)^3 = 5^(1/3)3 to hold so (5^1/3)^3 must equal 5 (SAT® Content  PAM.06).
 Background Info.
 Check for Understanding: Rational Exponents: Unit Fractions
 Review/Rewind: Basic Fractional Exponents
 Enrichment Tasks: Evaluating Exponential Expressions  Evaluating a Special Exponential Expression
N.RN.A.2
Rewrite expressions involving radicals and rational exponents using the properties of exponents (SAT® Content  PAM.06).
 Background Info.
 Check for Understanding: Simplifying SquareRoot Expressions  Simplifying Rational Exponent Expressions
 Review/Rewind: Understanding Square Roots
 Enrichment Tasks: Kelper's Third Law of Motion  Checking a Calculation of a Decimal Exponent
What are some signs of student mastery?

Tools & Technology
Desmos is a free online graphing calculator that works on any computer or tablet without requiring any downloads. A FREE Desmos iPad app is available too! Who Wants to be a Millionaire Square Root Functions  This online game uses the "Who Wants to Be a Millionaire" game to answer questions and earn money for Square Root Functions. This game does not require a download and is free. Exponential Graphs  This free online program will help students match the exponential function to the curve. This program does not require a download and has an easy, medium, and hard setting. 