Learning Resources

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Outcomes

In this lesson you will learn

  • a review of the absolute-value function
  • the concept of a piecewise function

By the end of this section students will be able to:

  • model problem situations with combinations and compositions of functions
  • analyze relations, functions, and their graphs
  • use tables and graphs as tools to interpret expressions
  • investigate and interpret combinations and compositions of functions
  • analyze and solve polynomial, rational, irrational, absolute value, and trigonometric equations
  • analyze and solve polynomial, rational, irrational, and absolute value inequalities

Introduction

In this section you will, first of all, review the absolute-value of linear functions. You will then extend your understanding by applying absolute-value to non-linear functions. Equations and inequalities involving absolute-value will also be solved.

This section of study requires about 3 hours for completion.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

  • how to graph linear absolute-value functions
  • absolute-value of a real number
  • slopes of tangents
  • domain
  • definition of the derivative
  • right and left hand limits