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 real-world 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 real-world 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 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 real-world 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)
- Check for Understanding: Evaluating Inverse Functions | Graph Quadratics | Graph Absolute Value Functions
- Review/Rewind: Intro to Inverse Functions | Intro to Parabola Transformations
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.
- 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
Model real-world data with functions. Justify why the model is most appropriate for the problem situation.
- Check for Understanding: Interpret Quadratic Models |
- Review/Rewind: Mosquito
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! |