Chapter 2: Manipulating Functions

Contents

Overview

You may end up with a function that has a ton of extra stuff in its definition, and want to make it a bit simpler. Good news! There’s plenty of techniques to express the same model in simpler ways, using proven techniques like combining like terms, factoring, distribution and more. Let’s get started.

Conventions

TODO: Move this somewhere better than the intro.

There are two important conventions in algebra to know:

  1. In any given term, variables are ordered alphabetically.
    1. For instance, you would write: x + y + z, not z + y + x.
  2. In any given expression, terms are ordered from highest power to lowest power (or lowest power to highest power)
    1. For instance, you would write: x^3 + x^2 + y^2 + xy + x + y or x + y + xy + x^2 + y^2 + x^3
    2. This “power” here is referred to as the term’s degree (a concept discussed in Polynomials).

Closing

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