TI-84 Workshop Notes
(also good for TI-83 and TI-83+)
© 2005-06 Dr. Robert J. Rapalje
Seminole State College of Florida
Sanford, Florida 32773
PART II: Graphing
Notice that there are five buttons across the top of the
calculator right below the display screen. These buttons are labeled
[Y=] [WINDOW] [ZOOM] [TRACE] [GRAPH]
Notice also that above the buttons, in a color that matches the
[2nd] button, are the labels:
[STAT PLOT F1] [TBLSET F2] [FORMAT F3] [CALC F4] [TABLE F5]
Before you can graph with the calculator, you must enter the
equation by pressing the [Y= ], also called the [F1], button. If the
calculator has been used before, the calculator will show the equation of
the previous graph entered in the calculator. New or cleared calculators
will show only the basic graph menu as shown below.
If the graphing component of the calculator has been used
before, then any previous graphs will be listed in Y1=, Y2=, etc. For any
of these equations that may need clearing, use the down arrow to move down
to whatever lines need clearing, and press [CLEAR] for each one.
Now, use the arrow key (if necessary) to return to the line with Y1=, and
type in the new equation to be graphed, as illustrated in the following
examples. Before beginning, find the second button in the second column [X,
T, θ, η], which means “x-variable.” When you type a variable in
order to draw a graph, this is the button to use!
1.
Graph 
. If you have not already done so, press the [F1 y= ]
button, and clear whatever might already be in the calculator in any of the
y= lines.
Next,
either press [x-variable] [^] [2], or equivalently press [x-variable]
[
].
Once you have entered the equation you wish to graph, press [F5
GRAPH]. In most cases you will get the graph below.
1a). If you do NOT get the graph pictured above, perhaps your
calculator is not in the standard window.
To standardize the window, press [F3 ZOOM] , and a menu drops
down . See the first menu listed below. Notice the arrow after the 7.
This indicates that there are MORE selections, that you can access by
pressing the up or down arrow (see the second menu listed below).
So, to standardize the window, press [F3 ZOOM], then [6:
ZStandard]. This process will correct most of the graphing problems. Be
sure you have the equation typed correctly, and make sure you have the right
window for the calculator—more on that later!
b)
There is another source of errors that you may encounter, and this
is the DIMENSION ERROR. You have a DIMENSION ERROR if your calculator gives
you this screen when you press [F5 GRAPH]:
Your only option is to press [ENTER] and Quit. To correct this
dimension error, press [2nd] [F1 STAT PLOT]. What appears on
the calculator screen is a summary of the “STAT PLOTS’ for the calculator.
In order to do graphing with the calculator, all the stat plots should be
[Off]. See the illustrations below. The illustration on the left, with all
of the plots set to [Off], is the way the calculator should be, but if,
perchance, one of your plots was accidentally turned on, it might look like
the illustration at the right. If this occurs, then scroll down to the plot
that is turned [On], and turn it [Off]. Then the calculator will graph as
it is supposed to graph, assuming you have the correct equation and an
appropriate window.
Press [CLEAR] to get out of this menu and return to a blank screen.
2. Graph
. Notice that this is “minus 4,” and not a “negative 4.”
Begin with [F1 y =], and
[CLEAR] if you want to clear the previous equation. Next, press [x-variable]
[] [— (minus)] [4], and [F5 GRAPH] to sketch the graph.
The graph should be as the one below.
3. Graph
. Notice that this is “negative
,” and not a “minus.”
Begin with [F1 y =], and
[CLEAR]. Press [(-)] [x-variable] [] [+] [4].
Press [F5 GRAPH] to sketch
the graph.
4. Graph
.
Begin with [F1 y =], and
[CLEAR]. Press [x-variable] []
[[— (minus)] [16], and [F5
GRAPH] to sketch the graph.
Notice that in the standard
graph window, you can’t even see the bottom of the graph. Sometimes it
helps to adjust the window. You may want to do this by pressing [F3 ZOOM]
followed by [F3 Zoom Out] to zoom out.
Or even better, press [F2
WIND] . The following menu drops down:
As you can see, the “standard window” shows the
graph with values of x from a minimum of –10 to a maximum of 10 with a scale
of 1. The y values go from minimum of –10 to a maximum of 10 with a scale
of 1. Xres controls resolution. Of course, you can easily change these to
set your window depending upon what you want to see. Having seen that the
previous graph is “cut off” at the bottom, maybe it would be a good idea to
extend the graph down to –20 instead of –10. To do this, just press the
down arrow three times, down to Ymin = -10. With the cursor flashing on
“Ymin = -10”, type [(-)20] [ENTER]. With the window set to your liking,
press [F5 GRAPH], and the calculator gives the graph you can see.
Notice in the graph below,
the x units are much larger than the y units, and therefore,
the graph is NOT drawn to scale.
If you want to see what the
graph really looks like, drawn to scale, you can go to “zoom square.” This
simply means that the x and y axes have equal units (unlike in the window
shown above!), and therefore the window is “square.” To do this, press [F3
ZOOM]. From the menu that drops down, select [5: ZSquare].
The graph really looks like
this. This is the window [F2 WINDOW]
MOST IMPORTANTLY, remember
that this is now your “new” window for future graphs. The next time you
draw a graph, after you enter the new equation, you should standardize the
window: [F3 ZOOM] [6: ZStandard].
5. Graph
.
As always begin with [F1 y =] [CLEAR] to clear the previous
equation.
Type the equation, using a
minus sign: [x-variable] [^] [3] [—] [4] [x-variable].
Remember that in the last
graph you changed the window, so now you should return to a standard
window: [F3 ZOOM] [6: ZStandard].
6. Graph
. Of course this is a straight line.
[F1 y =] [CLEAR] [3] [÷] [4] [x-variable]
[+] [4] [F5 GRAPH]
Standard Zoom
In case you are interested in seeing exactly how steep the line
really is (
), unbiased by the unequal units of the x and y axes, you
might want to graph this with a “zoom square”! You do this by pressing:
[F3 ZOOM] [5: ZSquare].
Zoom Square
Now, how do you change it
back to the Standard Zoom?
[F3 ZOOM] [6: ZStandard].
7. Graph
.
[F1 y =] [CLEAR] [2nd] [
]
[x-variable] [ )] [F5 GRAPH]
Notice that when you pressed the []
button, what you actually got was a [
] with an open parentheses included in it. This means
that after you type the [x] you should close the parentheses.
However, if you do NOT close the parentheses, then the calculator
automatically closes all parentheses at the end, and in this case it will
not make any difference in the graph. Usually it DOES make a difference, so
this is a good habit to have in graphing with this calculator!!
8.
Graph 
and compare to 
. How these are different?
First, graph
, which has only the x within the square root sign!
[F1 y =] [CLEAR] [2nd] []
[x-variable] [ )] [+] [4] [F5 GRAPH]
As in the previous example, notice that when you pressed the []
button, what you actually got was a [] with an open parentheses included in it. This means
that after you type the [x] you MUST close the parentheses. In this
case, it DOES make a difference! If you don’t close the parentheses, it’s
wrong!!
Second, graph
, which has the x and the 4 within the square root
sign! [F1 y =] [CLEAR] [2nd] []
[x-variable] [+] [4] [ )] [F5 GRAPH]
Notice that both of these
graphs are the same “shape” as .
The difference is that with , the graph is moved up 4 units, whereas with the graph
of , the graph is moved 4 units to the left!
9.
Graph 
and
compare to 
and 
. Do you see how these are different?
There are two easy ways to find absolute value on the
calculator. You can go to catalog, which is [2nd] [(decimal
point)] . The [CATALOG] menu is listed in alphabetical order, and the
calculator should go directly to [abs( ] . A second way to find [abs( ] is
by way of [MATH], [right arrow] to [NUM] , and again [abs( ] is the first
item in the menu that drops down.
Now, graph .
[F1 y =] [CLEAR] [2nd] [CATALOG] [abs(] [x-var]
[ )] [F5 GRAPH]
Now, graph .
[F1 y =] [CLEAR] [2nd] [CATALOG] [abs(] [x-var]
[ )] [] [4] [F5 GRAPH]
Now, graph .
[F1 y =] [CLEAR] [2nd] [CATALOG] [abs(] [x-var]
[] [4] [ )] [F5 GRAPH]
10. Graph
,
and compare to 
Remember that you access the
and 
functions by way of [MATH]. It is important also to
notice that the while the 
comes with a “3” for cube root and an open parentheses,
for the , the button to use is [5:
] which does NOT have either the “4” nor the open
parentheses.
First graph .
[F1 y =] [CLEAR] [2nd] [MATH] [4:
]
[x-variable] [ )] [F5 GRAPH]
Notice that when you pressed the []
button, an open parentheses was included in it. This means that, as with
the of the previous example, after you type the [x],
you should close the parentheses. Remember also that if you do NOT close
the parentheses, then the calculator automatically closes all parentheses at
the end, and in this case it will not make any difference in the graph.
Second, graph . Before you go to the [MATH] menu, you must enter the
index of the radical. You MUST begin with the “4” before the [MATH] menu.
[F1 y =] [CLEAR] [4] [MATH] [5:
] [x-var] [F5 GRAPH]
Notice that in this case, there are NO parentheses! Since the
calculator did NOT open parentheses, there is NO closed parenthesis, as
there was in the previous example. If you try to close parenthesis when
there was no open parenthesis, it’s wrong, and you will get an error message
telling you about it!!
From these graphs, you can
see that for ,
x≥0, but for, x can be any real number.