Course 3 Unit 6 - Families of Functions
1st Edition

Families of Functions is the third unit from the algebra and functions strand in Course 3. Students are now prepared to synthesize, formalize, and extend the toolkit of function models studied in Courses 1-3. (See the descriptions of Course 3 Units.)

Unit Overview

Families of Functions reviews and extends student understanding of the basic function families and develops student ability to adjust function rules to match patterns in tables, graphs, and problem conditions. New function models introduced in this unit are the absolute value function and the square root function.

Unit Objectives
  • To describe the table and graph patterns expected in linear, direct power, inverse power, exponential, sine, cosine, absolute value, and square root models, given the corresponding algebraic rules in function form
  • To identify a function as a variation of a basic family of functions
  • To recognize how the patterns in graphs, tables, and rules of functions relate to the functions' transformed graphs, tables, and rules
  • To write function rules which are reflections across the x-axis, translations, or stretches (or combinations of these transformations) of basic functions
  • To apply all of the transformations above as they relate to real-world situations

Sample Overview

This sample material is the first investigation of Lesson 1, "Function Models Revisited." In this investigation, students model and answer questions about contexts using linear, exponential, and power functions.

Instructional Design

Throughout the curriculum, interesting problem contexts serve as the foundation for instruction. As lessons unfold around these problem situations, classroom instruction tends to follow a common pattern as elaborated under Instructional Design.

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How the Algebra and Functions Strand Continues

Four units in Course 4 extend student understanding of algebra and function concepts in preparation for post-secondary education. Students develop understanding of the fundamental concepts underlying calculus, of inverse functions, and of logarithmic functions and their use in modeling and analyzing problem situations. Students also extend their ability to use polynomial and rational functions to solve problems and to manipulate symbolic representations of exponential, logarithmic, and trigonometric functions.

A unit that develops understanding and skill in the use of standard spreadsheet operations while reviewing and extending many of the basic algebra topics from Courses 1-3 is included for students intending to pursue programs in social, management, and some of the health sciences or humanities.

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