Chapter+02+Notes

Below are the links for the notes for Chapter 2. Again, each section should have its own note page, this time without the solutions to the assigned homework.

Chapter 2 moves us into our first major topic of discussion: Functions, Graphs and Equations. Each section comes as follows:

Here we speak of the differences between Relations and Functions. Relations are when two items have some kind of common connection. We might know what the connection is and we might not. A function is a special type of relation where for each input item there is at most one output. To understand the difference we need only ask if in normal situations is there only one possible answer (my age if you know my birthdate) or can there be more than one (a person's eye color if you know his or her hair color).

Now we are looking at our first type of equation. These will all form a straight line with no curves or bends in them. Three types of general linear equations are discussed including Standared Form (//Ax + By = C// where //A, B,// and //C// are all real numbers and we do not have //A = B = 0// at one time), Point-Slope Form (//y - y1 = m(x-x1)// with the slope being //m// and passing through the point (//x1, y1)),// and Slope-Intercept Form (//y = mx// //+ b// with a slope of //m// and a //y// - intercept at the point (0, //b//)).

This is a special type of Slope-Intercept equation where the //y// - intercept is always 0. The ratio of //y/////x// remains constant throughout all points on the line. This ratio is called //k// and it is the slope of the line.

This section talk about how we can use linear equations to represent the world around us. It also discusses scatter plots and the ways of interpreting them.

Now we are beginning to combine the ideas that we explored in Chapter 1. We are working with absolute values in two variable equations to create some interesting graphs. This type of graph will come to a point (called the vertex) and open either up or down. Learning the formatting of this type of graph does take a little practice, but they can be done. Be careful to watch your signs.

In this section we learn how we can move the graphs of our basic functions from one place on the coordinate plane to another. There are rules that govern these movements and they are very helpful to memorize and use for future times. These rules and patterns will show up again in the future as we begin to explore other types of functions and graphs.

In this section we begin to look at linear inequalities. While these are not technically functions they follow many of the construction methods and practices as standard linear functions. Several examples are given that may be helpful to those students that are struggling.

Continuing our discussion of inquality graphin we turn here to absolute value inequalities. The methods are very similar and the results come out about the same. There is one small twist to follow and an example of writing inequalities form the graphs that are provided.