Theory of Graphs and Graphing Utilities

Graphs and Graphing Utilities:


There are many types of graphs which the TI-82 or TI-83 will do, however they are accessed from similar key. The [y=] key and the [2nd] [y=] or [StatPlot] key. The two main types of plots might cause confusion whenever mixed; therefore it is best to turn off all needless plots before trying to graph an equation.

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

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

Graphing Equations with the Calculator:

Equations should be solved explicitly for y before being put into the calculator. In another words, y should be written as the function of x before entering the equation to the calculator.

Sometimes, equations cannot be solved for y. And in other times, the outcome is not a function. In this condition, you might require two y functions.

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

Whenever you solve the above equation, you obtain two values for y. Place the positive square root in y1and negative square root in y2. Otherwise, you can specify that y2= -y1. On TI-82, the y1 variable can be found beneath [2nd] [Vars] (or [Y-Vars]), Function. On TI-83, it is found beneath [Vars], Y-Vars and Function.

Zoom Settings:

There are some zoom settings which we will be using in this class.


The standard zoom setting sets the domain and range to [-10,10] and scale to 1. When you are not well-known with interval notation [-10,10].

Whenever moving the cursor in standard setting, the x-step is 0.21276596 and y-step is equal to 0.32258065. These are not ‘nice’ values, and frequently cause problems whenever trying to find precise values by tracing. They as well cause problems with graph whenever there are vertical asymptotes (that is, rational expressions) or at endpoints of domain.


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

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


As the size of screen is not similar, graphs encompass a tendency to not come out looking right. The square zoom setting is a manner to remedy that.

In decimal setting, the horizontal and vertical steps are both 0.1, therefore the images will appear square, however in the standard setting, and the horizontal and vertical steps are 0.213 and 0.323 correspondingly.

The square decimal leaves the bigger interval of the domain or range alone and modifies the settings on the smaller one. When the domain and range are of similar length (as in the standard setting), the domain is modified.

Zoom Out/Zoom In:

If you wish to maintain a square setting, however you require a bigger part of the viewing window to be exhibit; we can utilize the Zoom Out or Zoom In settings. Each of such need a position to zoom in or out about. Therefore, after you select the Zoom In or Zoom Out, you will need to place the cursor to where you want the center of zoom to be and hit the enter.

The zoom factor is as four. That is, when you zoom out, you will see 16 times as much area (that is, four times the horizontal and four times the vertical make sixteen times the area). As an illustration, suppose your domain is [-10,10] and your range is [-5,5]. When you zoom out with the origin as the center of zoom, your new domain will be [-40,40] and the new range will be [-20,20].

Whenever zooming in, the factor is one-fourth. In another words, a zoom in completed after a zoom out (with similar center for both) will return the prior settings.


The zoom box option is similar to the zoom in option, apart from that you specify two corners of a box, and then the area among those corners is exhibited.


The zoom statistics setting is helpful whenever you encompass a statistical plot which you want to comprise all the data for. The plot will set the Xmin and Xmax and hence all of the data is visible. When you are graphing a scatter plot, and hence there are both x and y data values, then Ymin and Ymax will as well be changed and hence all the data is visible.


It sets the domain to be from -2π to +2π with scale to be π/2. The range is [-4,4] with the scale of 1. This is a good setting to use whenever graphing trigonometric functions.

Determining Viewing Window:

When you are trying to find out what the viewing window is, you must place the equation to the calculator and hence you will be able to view when the graph matches the picture. Taken into account, the number of tick marks and the minimum and maximum settings.

The very first thing to do is try to determine various important points on the graph such as y-intercepts, x-intercepts or maximums and minimums. When you can figure out where it is at on graph from the calculator, you can then figure out what the scale is. Once you have that, it is pretty simple to find the viewing window by simply counting the number of ticks to each and every side of zero.

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