Chapter+07+Notes

As we begin the second semester of this class we pick up right where we left off. In Chapter 7 we are to continue our study of graphs involving exponents. This chapter deals with rational exponents in all of their forms, including radicals.

Our first lesosn covers the idea of how to find different roots. Roots are the means by which we undo the exponents that we have previously worked with. We are familiar with square roots, but now we will work with roots for higher dimensions.

The Second lesson looks at the properties and rules that govern the multiplication and division of radical expressions. Many of these we know from previous exposure and work in math.

The first half of lesson three deals with adding and subtracting radical expressions. The thing to remember here is that like normal numbers, we must have like terms to carry out these opperations.

The second half of the third lesson deals with multiplying and dividing binomial radical expressions. These are done using the FOIL method or traditional long multiplication and the concept of conjugates.

Lesson four goes into the situations when the numerator of our rational exponent is not a 1. In these cases we are both finding a root and raising to a power.

Now that we have gotten ourselves familiar with radical expressions we will apply our knowledge to situations where we must solve equations with the variable being raised to a rational power.

The first part of lesson six deals with the four basic operations we can do with functions. Many of these we know from previous work, but this section formalizes our ideas.

Part two of lesson six works with function composition. How can we work with a chain of functions where the output from the first becomes the input for the second, and so on?

Lesson seven deals with a concept called inverse functions and relations. These work in the way that an inverse function will undo a normal function. It also deals with how to find an inverse if you are given the function.

The last lesson of the chapter finally comes to graphing of radical functions. There are differences if the index of the function if odd or even, and this section deals with those differences.