## Unit 3: Function Synthesis, Derivations in Analytic Geometry, Series and Limits

### Overview

*According to Galileo, “mathematics is the language with which God wrote the Universe.” Math is about relationships—the interaction between quantities, variables, and change. Math is about patterns. Math is about logic. One of the most fundamental mathematical concepts that embodies pattern, logic, and relationship is the function. You have modeled real relationships with many functions—linear, exponential, quadratic, radical, trigonometric, and now rational. The return on invested money, Galileo’s very own projected path of a cannonball, the decay of a radioactive substance over time, oscillations of a pendulum—all of these are function relationships!*

**Developed By:** Megan Hott & Sean Freeland

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## Pre-Unit Assessment

## Lesson 1

Rational Behavior

## Lesson 2

Graphing Rational Functions

## Lesson 3

Creating and Composing Functions

## Lesson 4

Inverses of Functions

## Lesson 5

Ellipses, Hyperbolas, and Cavalieri’s Principle

## Lesson 6

Sequences and Series