Mathematical Analysis (Honors)
Unit 1: Graphical Analysis of Functions
In this unit, students analyze the key features of graphs of functions and make connections between domain, range, relative extrema, intervals increasing/decreasing, end behavior, continuity, zeros, and symmetry. Students create an equation, graph, table, or verbal description given key properties including increasing or decreasing behavior, the sign of the leading coefficient, degree, and end behavior.
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.
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:
Recognize and sketch various transformations of common functions.
MA.AF.A.1
Recognize graphs and transformations of common functions and sketch the graph of a transformed function. (Quadratic, Absolute Value, Power)
Build and interpret functions that model relationships between two quantities.
PC.AF.A.1
Identify key features of functions, including domain, range, end behavior, local (relative) and/or absolute extrema, continuity, zeros, symmetry, asymptotes, and whether the function is even/odd.
Model realworld data with functions. Justify why the model is most appropriate for the problem situation.
Recognize and sketch various transformations of common functions.
MA.AF.A.1
Recognize graphs and transformations of common functions and sketch the graph of a transformed function. (Quadratic, Absolute Value, Power)
 Background Info.
 Check for Understanding: Evaluating Inverse Functions  Graph Quadratics  Graph Absolute Value Functions
 Review/Rewind: Intro to Inverse Functions  Intro to Parabola Transformations
 Enrichment Tasks: Identifying Quadratic Functions
Build and interpret functions that model relationships between two quantities.
PC.AF.A.1
Identify key features of functions, including domain, range, end behavior, local (relative) and/or absolute extrema, continuity, zeros, symmetry, asymptotes, and whether the function is even/odd.
 Background Info.
 Check for Understanding: Find features of quadratic functions  Domain and Range  Relative Maxima and Minima  Absolute Minima and Maxima  Positive and Negative Intervals  Increasing and Decreasing Intervals 
 Review/Rewind: Intro to Positive, Negative, Increasing and Decreasing Intervals
 Enrichment Tasks: Graphing Stories 
Model realworld data with functions. Justify why the model is most appropriate for the problem situation.
 Background Info.
 Check for Understanding: Interpret Quadratic Models 
 Review/Rewind: Mosquito
 Enrichment Tasks: Throwing Baseballs
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! 