# 1.1 - Graphs and Graphing Utilities

## TI-82

There are several kinds of graphs that the TI-82 or TI-83 will do, but they are accessed from the same key. The [y=] key and the [2nd] [y=] or [StatPlot] key. The two major kinds of plots may cause confusion when mixed, so it is best to turn off all unnecessary plots before trying to graph an equation.

To turn off all statistical plots, hit [StatPlot] and choose option 4 - PlotsOff. Hit enter to finish the command.

To turn off a regular plot, one can either hit [Clear] while on an equation, or arrow to the left so that the cursor is on the equal sign, and press enter to toggle the display of that equation.

## Graphing Equations with the Calculator

Equations must be solved explicitly for y before being placed into the calculator. In other words, y must be written as a function of x before entering the equation into the calculator.

Sometimes, equations can't be solved for y. Other times, the result is not a function. In this case, you may need two y functions.

x2 + y2 = 16 has the solutions y = + sqrt(16 - x2) and y = - sqrt(16 - x2)

When you solve the above equation, you get two values for y. Put the positive square root in y1and the negative square root in y2. Alternatively, you can specify that y2= -y1. On the TI-82, the y1 variable can be found under [2nd] [Vars] (or [Y-Vars]), Function. On the TI-83, it is found under [Vars], Y-Vars, Function.

## Zoom Settings

There are several zoom settings that we will be using in this class.

### Standard

The standard zoom setting sets the domain and range to [-10,10] and the scale to 1. If you're not familiar with the interval notation [-10,10], please refer to the preliminary chapter.

When moving the cursor in the standard setting, the x-step is 0.21276596 and the y-step is 0.32258065. These are not "nice" values, and often cause problems when trying to find exact values by tracing. They also cause problems with the graph when there are vertical asymptotes (rational expressions) or at the endpoints of the domain (as was illustrated in class with the circle).

### Decimal

The decimal zoom setting sets up the screen so that the x-step is 0.1 and the y-step is 0.1. This makes the values much nicer to look at, but gives you a much smaller window.

The domain for the decimal setting is [-4.7,4.7] and the range is [-3.1,3.1]. This also helps us figure out the size of the screen. If each pixel (dot on the screen) is 0.1 apart, then there are 95 pixels horizontally and 63 pixels vertically.

### Square

Because the size of the screen is not the same, graphs have a tendency to not come out looking right. The square zoom setting is a way to remedy that.

In the decimal setting, the horizontal and vertical steps are both 0.1, so the images will appear square, but in the standard setting, the horizontal and vertical steps are 0.213 and 0.323 respectively.

The square decimal leaves the larger interval of the domain or range alone and changes the settings on the smaller one. If the domain and range are the same length (as in a standard setting), the domain is changed.

### Zoom Out / Zoom In

If you want to maintain a square setting, but you need a larger portion of the viewing window to be shown, you can use the Zoom Out or Zoom In settings. Each of these require a position to zoom in or out about. So, after you choose the Zoom In or Zoom Out, you will need to position the cursor to where you want the center of the zoom to be and press enter.

The zoom factor is four. That is, if you zoom out, you will see sixteen times as much area (four times the horizontal and four times the vertical makes sixteen times the area). As an example, assume your domain is [-10,10] and your range is [-5,5]. If you zoom out with the origin as the center of the zoom, your new domain will be [-40,40] and hte new range will be [-20,20].

When zooming in, the factor is one-fourth. In other words, a zoom in done after a zoom out (with the same center for both) will return to the previous settings.

### Box

The zoom box option is like the zoom in option, except that you specify two corners of a box, and then the area between those corners is displayed.

### Stat

The zoom statistics setting is useful when you have a statistical plot that you want to include all the data for. The plot will set the Xmin and Xmax so that all of the data is visible. If you are graphing a scatter plot, so that there are both x and y data values, then the Ymin and Ymax will also be changed so that all of the data is visible.

### Trig

Sets the domain to be from -2π to +2π with the scale to be π/2. The range is [-4,4] with a scale of 1. This is a nice setting to use when graphing trigonometric functions, but we won't be doing that in this class, so you can pretty much ignore it.

## Determining the Viewing Window

When you're trying to determine what the viewing window is, you should put the equation into the calculator so that you will be able to see when the graph matches the picture. Take into account the number of tick marks and the min and max settings.

The first thing to do is try to find some important points on the graph like y-intercepts, x-intercepts, or maximums and minimums. If you can figure out where it's at on the graph from the calculator, you can then figure out what the scale is (how far apart the ticks are). Once you have that, it's pretty easy to find the viewing window by just counting the number of ticks to each side of zero.