Mission Statement | Math Monkey? | Getting Started | Screen Shots

## Graphing

by Derek

For being the most important part of a graphing calculator, I've found that a lot of people don't realy know how to make their math monkey graph. I'll give you a quick tour or you can look at our more in depth sections on how to use: y=, the Stat Plot, window settings, Zoom, Format, Tables, and calculus functions.

#### Tour

Graphing is the primary function of the TI 83 and it does a good job of making all of graph functions easily accessible. In fact, all of the buttons you'll need to graph are on the top row just under the screen. The five buttons, left to right are: [y=], [Window], [ZOOM], [TRACE], and [GRAPH]. They each also have a secondary function, accessed by the [2nd] key. Left to right they are: [Stat Plot], [TBLSET](tablesetup), [Format], [Calc](calculus), and [Table]. Of course, we're assuming that you're working with function graphs (normal xy plane) since high school math doesn't really use anything else. The information on this page takes that in mind though most of what is mentioned here is useful in the other graphing modes.

To work with graphs, you really only need two of those, the [y=] and [Graph] buttons. Pressing [Graph] will bring up the graph window from where ever you happen to be at the time. Before you will any graphs though, you must go to the [y=] and type in the function. Once the function is entered in the [y=], you can hit [Graph] and watch the calculator draw your function. On some occasions, you may not see the function. All you have to do is fiddle with your window settings or change the zoom and it will be alright.

So now you have your graph on the screen, you want to look at it right? That's where [Trace] comes in handy. In the graph window, if you press [Trace], a cursor will appear on the line with the xy coordinates of the point at the bottom of the screen. To 'browse' the line, just press the [<] [>] arrow keys. The cursor will travel along the line with its current position noted at the bottom of the screen. If you have more than one function on the graph, you can switch which function you're tracing by pressing the [^] [v] arrow keys and it will cycle through the the functions in the order they appear in the [y=] menu. If you're tracing to a specific x point, just type that number in and the trace will jump straight there. This is good for finding y values but only works if that point is on the screen.

#### Y=

You've already seen how easy it is to graph a function but there's more to the [y=] than that. Here's some other neat things you can do.
Moving the cursor up and down allows you to write, edit, or delete any of up to 10 functions you have stored in you y=. Did you know that you don't have to show all those functions at once? You are allowed to pick and chose which functions are graphed. Simply move the cursor to the far left of the function, then move it left once more so that it's flashing over the '='. If the = is highlighted, that function is enabled, will be graphed. Otherwise the function is disabled and won't be graphed. With the cursor over the =, simply press the [Enter] to toggle that function's status.

Another neat thing you can do with functions is set their line style. Press the left arrow once from the = and it will start blinking over that little slanted line to the left of the function name (y1...y0). The little slant is showing you what style the line will be graphed in. Pressing [Enter] here will cycle through the options:
normal (thin slanted line): draws your normal, everyday, Joe Smo line
thick (thick slanted line): draws a double wide version of the normal
shade up (black triangle pointed up, right): shades above the function. note: shades aren't solid black so you can do multiple shades and still see where they overlap
path (looks like and O with a hyphen in front of it): draws a normal line with a circle cursor at the leading edge, useful if you have several graphs cluttered together.
animate(just an O): same as above except without the line. I've never really used these except for fun. I once drew a cannon and had a parabolic function (ie: x²...) coming 'out' of it set to this line style. I had many people convinced that I wrote a program for shooting a ball out of a cannon:)
dot(dotted line): creates a dotted line

You can also enable or disable your stat plots from the y= menu. Just move the cursor above the y1 function so that it's over Plot1, Plot2, or Plot3. Hit [Enter] to toggle them. Personally, I prefer to do this from the Stat Plot menu.

One last thing you can do is use variables. I'm not talking of x or y or whatever else you've worked with. Your calculator stores each function in the y= menu as a y= variable (oddly enough, named y1 through y0). This means you can use one function as part of another function. When editing a function, insert a stored function by: pressing [VARS], selecting Y-VARS and then 1:Function. Just pick the function you want to insert and viola. This is real useful if you have similar functions or you have overlapping functions. Say y1 is the function x² and you want to overlap a function that's 2 points higher. Within y2, you can insert 'y1' and add on '+2' and it will work the same as 'x²+2' without all the extra typing.

If a new function is similar to a stored function, but slightly different, you still don't have to retype the whole thing. Start your new function, press [2nd][RCL] and then recall the function you want the same as above. It retypes the function for you to be edited at your pleasure.

#### Stat Plot

Stat Plot allows you to use any lists you've made with a graph. Usually you'll have two lists, one with the x portion of a set of coordinates, the other with the y portion. Pressing [2nd][Stat Plot] brings up five options, the first three allow you to edit the three stat plots, the fourth turns all of the plots off, while the fifth turns them all on.

While editing a plot, you can enable/disable (as do in the y= menu), chose style of plot - whether you want point, connected point, or various bar graphs - and set which list has the values you're using for your plot. Some graphs styles also let you chose how points appear.

You can set the lists used for your plot by moving the cursor to the appropriate place and either pressing [2nd][L1] (or [L2]-[L6]) or by selecting a named list from [2nd][LIST]NAMES

#### Window settings

The graph you want to see isn't all ways going to show up in the standard window. Sure, you can change your zoom but sometimes you want to tweak things to your own liking. Changing the window settings can be better than zoom and is often faster, provided you know what you want. If it's hit n miss, maybe zoom is the better choice.

Here's the window settings and what they mean. Just move the cursor up and down and change the numbers as you wish. You can always go back to the default with zoom standard.
Xmin: the minimum x value, far left of graph
Xmax: the maximum x value, far right of graph
Xscl: sets the spacing for the tick marks on the x axis
Ymin: the minimum y value, far bottom of graph
Ymax: the maximum y value, far top of graph
Yscl: sets the spacing for the tick marks on the y axis
Xres: sets the resolution of graph from 1-8. 1 is the best while 8 the worst (I don't know why you'd want to change this)

#### Zoom

If the graph is to big or small for the graph window, you have to zoom to see it. Other times you may want to see one part a little more closer or maybe see the whole thing at once. The thing is, there's so many 'zooms' to choose from. Our little guide here should help you to pick the right one for the job.

[ZOOM]
ZBox: lets you set a box around what you want to zoom in to - great if you want to look at one part of the graph
Zoom In: zooms in on a point you select with the cursor
Zoom Out: zooms out from a point you select with the cursor
ZDecimal: sets the window settings so that each pixel on the screen is the same as .1 - I've never really used this but if you wanted precision with a draw program perhaps
ZSquare: changes the window settings so they are proportional (not a rectangle). Added bonus: circles look like circles and not ovals!
ZStandard: resets your window settings to the default
ZTrig: changes the windows settings to adjust for pi - allows you to see those trig functions
ZInteger: I'm not sure why they stuck this in here but it does change your scales to 10
ZoomStat: changes the viewing window to fit your current stat plot, very useful
ZoomFit: when all else fails. this is good to use when you're not sure where the function is. it will give a good over view of the function but usually lacks details. a good start

Though it's something I've never really done, you can save and recall window settings from [ZOOM] MEMORY. It also lets you tweak how it zooms in and out!

#### window Format

Changing your window format is a lot like changing the calculator's modes. Each row is a toggle and here's what they do:

RectGC/PolarGC: Determines whether rectangular coordinates or polar coordinates are displayed.
CoordOn/Off: Whether or not the coordinates are displayed at the bottom of the screen.
GridOff/On: Turns the grid on or off. It looks neat on but is slower.
AxesOn/Off: Turns the axes on or off. I sometimes turn it off if I'm zoomed way out the function is scrunched against it.
LabelOff/On: Turns the axes's lables on and off. It's really an annoyance on.
ExprOn/Off: When you're working with a function (like tracing it) this will determine whether or not the function it self will be displayed. Good for remembering what you're working with.

#### Tables

If you'd rather look at a bunch of values than a graph, you can look at the table. [2nd] [Table] It just lists x and y values and allows you to scroll up and down. You can fiddle with the starting number and how much the table changes between sets of points. This is done in the table setup: [2nd] [TBLSET].

#### Calculus Functions

Ah, one of the best parts of the graph capabilities: the calculus functions! It used to be that one had to work to find things such as where a line crosses the x axis or what the value is at the top of that little hump. Well, your calculator can do that to!

[2nd][CALC]
value: This works similar to trace but you just put the x value in.
zero: This finds where a function crosses or touches the x axis. You set the area to check (left and right bounds) and guess where to start. Guessing doesn't really matter but may speed things up.
minimum: Finds the minimum (lowest) point in a given area.
maximum: Finds the maximum (highest) point in a given area.
intersect: Finds the point of intersection of two functions. select which two by cycling though all the graphed functions with the up/down arrows and pressing enter for the two you wish. Be sure to guess close to the point of interest in case there's more than one.
dy/dx: (Calculus and above) finds the derivative at a point.
f(x)dx: (Calculus and above) Finds the Intergral for a range of x. Also a good way of finding the area underneath a function.

Wow! That's a lot, but you can go back to learn more if you want.