Unit 9: Modeling with Functions
Lesson Video
Focus Standards
Learning Focus
Additional Resources
Lesson 1: Function Family Reunion
A Solidify Understanding Task
Provides a review of familiar functions – their equations, graphs, and transformations. Solidifies previous observations about transformations, connects geometric transformations to function transformations, and confirms that transformations are consistent across all types of functions.
Explain function transformations across all function types.
How can I observe the transformations of functions when comparing tables of data?
Video: Shifting Functions
Lesson 2: You Are the Imagineer
A Develop Understanding Task
Surfaces ideas about the effects of combining standard functions using arithmetic operations by creating graphs of function combinations.
Predict and examine the graphical effects of adding or multiplying functions from two different function families.
How can we combine function types to describe more complicated real-world behavior?
Lesson 3 : The Bungee Jump Simulator
A Solidify Understanding Task
Solidifies thinking about combining functions through addition and multiplication by determining exact equations that would produce a given graph.
Write equations that would produce given graphs created by adding or multiplying two functions together.
What does it mean to “model with mathematics,” and what can I attend to in order to make my models more precise?
How do I attend to the details in the features of a graph produced by combining two functions so that I can write the equation of the combined function?
Lesson 4 : Composing and Decomposing
A Develop Understanding Task
Introduces composition as another way to combine functions and provides opportunity to compose functions together to model complex behavior.
Examine function composition in the context of a real-world scenario.
Are there ways to combine functions other than by adding, subtracting, multiplying, or dividing them?
How do I model contexts in which one function depends upon the output of another function?
Lesson 5 : Translating My Composition
A Solidify Understanding Task
Extends understanding of function composition by composing and decomposing a particular set of functions. Surfaces the idea that function composition is not commutative and that functions created by composition can be interpreted as transformations of parent functions.
Write and evaluate composite functions.
What can I learn about a composite function by attending to its component parts?
Lesson 6 : Different Combinations
A Practice Understanding Task
Provides practice of strategies for combining functions by addition, multiplication, and composition. Extends understanding of combining functions to graphs, tables, numbers, and equations.
Combine functions defined by graphs or tables.
How can I represent function addition and multiplication? How are these operations defined when the functions being added or multiplied are defined by graphs or tables?