Chapter+09+Notes

In Chapter 9 we will begin working with functions that have the variable in the denominator of a fraction. These are called Rational Functions.

To begin our study of Rational Functions, let's take a quick over view of the materials that will be studied. Look at each problem. If you understand it solve it. If you are not certain, write the questions that you have about the problem. When you finish, turn to Chapter 9 in your book and see if you can find answers to your questions.

Now that we have had a preview of the materials that we will see in Chapter 9, let's look at each in more detail. We will begin with section 1 which introduces us to the concept of reational functions throughInverse variations. Here we practice writing and finding inverse variations.

Now that we know direct and inverse variations we can write equations by combining them. These are called Combined Variations. This section uses descriptions of formulas and their interpretation into a written mathematical form.

As we continue our examination of inverse variations we will now turn our eyes to their graphs. The Features and characteristics of these graphs are slightly different than those previously studied and we shall begin this look at those that are centered around the origin.

The graphs of these functions can be translated with a vertical stretch as well as by using horizontal and vertical shifts. This lesson practices on those ideas.

Now that we have th ebasic functions of inverse variations down we can begin looking at the larger family of functions called Rational Functions. These functions will have asymptotes of different types, and here we look at these types and how to find them.

Now that we have all of the parts for constructing the graph of a rational function, let's actually do some. This lesson teaches how to put the parts together from what we learned in the last few sessions.

Part of working with rational expressions, equations and functions is that we will need to perform the basic mathematical operations with them from time to time. In this lesson we will be simplifying, multiplying, and dividing rational expressions.

In this lesson we are learning how to add and subtract rational expressions. Just as in adding, we need to have common denominators in order to make this possible. This worksheet will provide an example of how to do it and give some problems to practice with. If you need or want some extra practice, page 507 in the book provides some nice exercises. I suggest problems 4 - 21.

With the finer points f rational expressions now mastered we will move on to solving rational equations. These can look much like proportions and can often be solved in similar manners. The over all idea is that once the denominators are equal to one another, all we need to do is make the numerators equal and we will be finished.