Welcome to Unit 2! In this unit we will learn all about Linear and Exponential functions. We will discuss what they are, what they are used for, and compare them. 

Initially you are going to think these sound a bit scary, but you've actually already been working with these functions. Linear Functions are what we call a continuous Arithmetic Sequence. Exponential Functions are just continuous Geometric Sequences. We will talk about what continuous and discrete mean this unit as well so don't worry if that doesn't make sense right now.

Unit 2 spends a few lessons discussing the very important Properties of Exponents that we have to follow. These rules are the laws of the exponents and dictate what we can and can't do.

Lesson 2

At the very end of the first lesson, we discuss Domain for the first time. The Domain of a function tells us which numbered are allowed to be used as inputs. For example, it would not make sense to find out how much money you make from working -3 hours, so the domain of hours worked can only contain positive numbers. This is a very important concept when we discuss discrete and continuous functions so make sure you watch those videos in lesson 1 first. You will learn about this in the video about Set Builder Notation.

When we discuss domain, it's important to know about the different types of numbers, so I have also included a video about that. 

Domain and set builder notation are very important to understand and be able to use. Here are some links to articles and practice problems that will be helpful. 

Determining Domain Word Problem

Set Builder Notation, Definition, Examples

Set Builder Notation-Mathisfun.com

Lesson 4

The next few lessons are going to be all about exponents. We will spend time each of the rules of exponents individually, starting with rational exponents, then negative exponents, and then looking at what happens when we multiply and divide exponents. 

To start, Rational Exponents. When we say rational, that usually means a fraction. So we are going to figure out what it means to have a fraction in our exponent.

Lesson 6

Nothing new in this lesson! We are using what we learned in Lessons 4 and 5 and applying it to rational exponents. Do the rules still hold up when used on Fractions? Absolutely. In this lesson we spend most of our time working with banking questions to examine exponents. I wasn't quite able to find some videos that explained it very well, so here are some other videos about banking that I think could be helpful.

Lesson 8

In lesson 8 we look at business plans as a way to once again compare linear and exponential functions. This time, we particularly want to look at their growth. Which one grows faster? Which one grows larger over time? That's what we want to know.

Lesson 10

This lesson is all about looking for patterns that make writing equations of linear functions helpful to us. I think this is a good time to review the slope formula, and point-slope form. These will both be needed for your test.