Objective -- Rational Functions (3 Weeks)

[Scope and Sequence]
[Foundations For Functions][Parameter Changes][Linear][Quad Functions][Square Root Functions][Rational Functions][Exponential & Logarithmic][Conics]

This unit includes equations, inequalities, and systems. There should be an emphasis on the connection between the 5 representations: graph, table, problem situation, pictorial, symbolic. Within this unit, connections to foundations for functions and how all functions have same traits should be made.
Rational Functions (3 Weeks)
Objective	TEKS	TEKS Clarification	TAKS Objective	SATEC Lesson/Resources	SATEC Correlated Assessment	Dana Center Assessments	Resources/Text
Identify and sketch the rational parent function.	2A.4A	Revisit data activity from Foundations for Functions and reinforce common function characteristics. Revisit data to extend the investigation of Rational Functions to include writing equations, graphing and translating functions, and analyzing parameter changes in the context of situations. · Investigation of graphs of rational functions is limited to f(x) = a/(x-h) + k Limitations on domain & range are limited to vertical and horizontal asymptotes. Adding & subtracting rational expressions is not required for solving rational equations unless it involves common denominators Compare direct & inverse variations in a given problem situation. (include both y = k/x and y = k/x² Use technology such as graphing calculators and/or computers to link multiple representations	Obj 1: Alg I A.1A, A.1B, A.1C, A.1D, A.1E Obj 2: Alg I A.2B, A.2C, A.2D, A.3A, A.3B, A.4A, A.4B	Fade Away! Stuff It!	Fade Away--Reflect and Apply		Algebra II Institute: Part A: II. 1.1 Graphing the Rational Function
Uses quotients to describe the graphs of rational functions, describe limitations of domain and range of rational functions, and examine asymptotic behavior.	2A.4A 2A.10A			Fade Away! Stuff It!	Fade Away--Reflect and Apply		Parameter Changes and Asymptotes
Investigate, describe and predict the effects of parameter changes on the rational function.	2A.4B					What is My Equation?	Parameter Changes and Asymptotes Calculator Exploration
For a given problem situation, analyze the various representations for the situation.	2A.10B 2A.10E			Fade Away! Stuff It!	Fade Away--Reflect and Apply	Saline Solution
For a given application, determine the independent and dependent variables and analyze the possible domain and range values and solutions appropriate for the given situation.	2A.10C			Fade Away! Stuff It!	Fade Away--Reflect and Apply	Pizza Pizza Wars Part 2. You are Toast, Dude
Solve rational equations using tables, graphs, and algebraic methods.	2A.10D			Fade Away! Stuff It!	Fade Away--Reflect and Apply
Analyze a situation modeled by a rational function, formulate an equation or inequality and solve the system problems	2A.10E 2A.10F			Fade Away! Stuff It!	Fade Away--Reflect and Apply	Paintings on the Wall
Use direct and inverse variations to solve problems	2A.10G
For a given application, identify the mathematical domain and range and the domain and range for the situation.	2A.1A			Fade Away! Stuff It!	Fade Away--Reflect and Apply
Collect and organize data, make scatterplots, fit the curve to a function, interpret the results, and model, predict, and make decisions.	2A.1B			Fade Away! Stuff It!	Fade Away--Reflect and Apply
Recognize that functions can be denoted in many forms: y =, d =, y= and f(x) = and determine which form is the most appropriate for a given situation.	2A.2C
Students perceive functions and equations as means for analyzing and understanding relationships and as a tool for expressing generalizations.	BU A3			Fade Away! Stuff It!	Fade Away--Reflect and Apply
Use a variety of representations, tools, and technology and model situations to solve problems.	BU A5			Fade Away! Stuff It!	Fade Away--Reflect and Apply
Use math processes throughout, including problem solving, computation, communication, connections, reasoning, multiple representations, modeling, and justification	BU A6			Fade Away! Stuff It!	Fade Away--Reflect and Apply

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