Graphing utilities such as graphing calculators and computers with graphing software are very valuable tools for visualizing mathematical principles, verifying solutions to equations, exploring mathematical ideas, and developing mathematical models. While graphing utilities are extremely helpful in learning mathematics, their use does not mean that learning algebra is any less important. In fact, the combination of knowledge of mathematics and the use of graphing utilities allows you to explore mathematics more easily and to a greater depth. If you are using a graphing utility in this course, it is up to you to learn its capabilities and to practice using this tool to enhance your mathematical learning.

This introduction gives a brief description of two basic features of your graphing utility: the equation editor and the table feature. If you will be using your graphing utility more extensively in Chapter 1, you may want to review Section 2.3. You may also find it helpful to consult the user's guide for your graphing utility. Additionally, graphing utility keystroke guides are available for most models, and your college library may have a videotape on how to use your graphing utility.

The Equation Editor

Many graphing utilities are designed to act as "function graphers." In Chapter 3, you will study functions and their graphs in detail. You may recall from previous courses that a function can be thought of as a rule that describes the relationship between two variables. These rules are frequently written in terms of x and y. For example, the equation y= 3x + 5 represents y as a function of x.

figure 1

Many graphing utilities have an equation editor that requires an equation to be written in "y=" form in order to be entered, as shown in Figure 1. (You should note that your equation editor screen may not look like the screen shown in Figure 1.) To determine exactly how to enter an equation into your graphing utility, consult your user's guide.



The Table Feature

Most graphing utilities have the capability to display a table of values with x and one or more y-values. These tables can be used to check solutions of an equation and to generate ordered pairs (x, y) to assist in graphing an equation.

To use the table feature, enter an equation in the equation editor in "y=" form. The table may have a setup screen, which will allow you to select the starting x-value and the table step or x-increment. You may then have an option to automatically generate values for x and y or to build your own table using the ASK mode. In the ASK mode, you enter a value for x and the graphing utility will display the y-value.

For example, enter the equation

figure 2

in the equation editor as shown in Figure 2. In the table setup screen, set the table to start at x= -4 and set the table step to 1. When you view the table, notice that the first x-value is -4 and each value after it increases by one. Also notice that the Y(sub)1(/sub) column gives the resulting y-value for each x-value, as shown in Figure 3. The table shows that the y-value when x=-2 is ERROR. This means that the variable x may not take on the value in this equation. You can use the arrows on the keypad to scroll through the table.

With the same equation in the equation editor, set the table to ASK mode. In this mode you do not need to set the starting x-value or the table step, since you are entering any value you choose for x. You may enter any real value for x- integers, fractions, decimals, irrational numbers, and so forth. If you enter x = 1 + , the graphing utility may rewrite the number as a decimal approximation, as shown in Figure 4. You can continue to build your own table by entering additional x-values in order to generate y-values.

figure 3	figure 4

If you have several equations in the equation editor, the table may generate y-values for each equation.

Before beginning Chapter 1, be sure you are familiar with the use of the equation editor and the table feature. Remember that the screens and names of features and modes may not be the same as your graphing utility, so you should always consult your user's guide for help.