Chapter 14 - Modeling with Functions
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"In this chapter, students explore various real-world and purely mathematical situations that are modeled with functions. Function composition is developed, and students apply function composition to solve contextual problems. Students also use functions to draw graphics, to model optimal solutions and self-similarity, and to study situations modeled by logistic growth, such as the spread of infectious diseases. Students end the chapter by choosing appropriate functions to model a variety of problem situations." Carnegie Textbook |
"You are looking at a picture of a cat looking at a picture of a cat looking at a picture of a cat . . . But you are also looking at a mathematical process of repetition and self-similarity called recursion" - Carnegie Textbook
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Lesson 14.1 - Composition of Functions
"Students are introduced to composition of functions in the context of combining coupons. Students then explore various characteristics of function composition, including using composition to verify that two functions are inverses." - Carnegie Textbook Lesson 14.2 - Art and Transformations
"In this lesson, students use their knowledge of function families and transformation function form to create graphics and to identify functions used to create them." - Carnegie Textbook Lesson 14.3 - Optimization
"In this lesson, students determine optimal solutions in real-world situations by modeling systems of inequalities and quadratic functions" - Carnegie Textbook |
Lesson 14.4 - Interpreting Graphs
"In this lesson, students study logistic functions in the contexts of population growth and the spread of infectious disease. " - Carnegie Textbook Lesson 14.5 - Fractals
"Students explore fractals in this lesson, including the Sierpinski Triangle, the Menger Sponge, and the Koch Snowflake. Students explore the sequences that model the perimeter, area, or volume of these objects and derive an explicit formula for the perimeter of the Sierpinski Triangle using sigma notation." - Carnegie Textbook Lesson 14.6 - Choosing Functions to Model Situations
"Students graph and analyze functions to model the speed of a rotor, the resistance of an electrical circuit, and the temperature of a liquid over time." - Carnegie Textbook |
