# Week 3

## Topics

This week, we will cover the remainder of Chapter 2. Specifically, we will look at

• Chapter 2-3, 2-4: Quadratic Functions
For quadratic functions we review vertex and intercepts.
• Chapter 2-4: Polynomial and Rational Functions
For general polynomial and rational functions we don't go into much detail. A rational function is a quotient of two polynomials.
For polynomials, we just look at the possible shapes of the graph, specifically the number of intercepts and turning points it can have. For rational functions, we look at the domain and at vertical and horizontal asymptotes.
• Chapter 2-5 : Exponential Functions
You have already seen the properties of exponential functions twice recently in appendix A (once for integer exponents, once for rational exponents), so those should be familiar. Now we look more at the properties of the graph of exponential functions.
Concentrate on learning the properties of bx with b>1. The graph of an exponential curve with b<1 is just the reflection in the y-axis of the exponential curve with 1/b>1. For example, (1/4)x is the same as 4-x.
All exponential graphs with b>1 look pretty much the same. The one with b=e is just a special case. e is an important number in mathematics that comes up in a lot of places where you wouldn't expect it; sort of like π.
The application to compound interest will come back in chapter 3 (which we won't cover until week 8). You can look ahead to chapter 3 for more explanations on compound interest, if you want.
• Chapter 2-6: Logarithmic Functions
This section is very important for solving equations involving exponentials. This material may not be as familiar to you as the previous topics, or maybe completely new.

## Assignments

Read the textbook and do HW 3 in MyMathLab.

Note that a hard deadline for homeworks kicks in this week. We let students add the course until the end of week 2, so we don't enforce homework deadlines until week 3. The homework for this week, as well as earlier weeks, is due by the end of week 3.

Last Updated: Wednesday, August 5, 2015