Graphing Functions on TI83/84
Copyright © 2001–2019 by Stan Brown
Copyright © 2001–2019 by Stan Brown
Summary: It’s pretty easy to produce some kind of graph on the TI83/84 for a given function. This page helps you with the tricks that might not be obvious. You’ll be able to find asymptotes, intercepts, intersections, roots, and so on.
See also:
Evaluating Functions with TI83/84
Graphing Piecewise Functions on TI83/84
The techniques in this note will work with any function, but for purposes of illustration, we’ll use
Step 1: Clear unwanted plots.
You need to look for any previously set plots that might interfere with your new one.  Press [Y= ] (the top left button).
Look at the top of
the screen. If any of Plot1 Plot2 Plot3 is highlighted,
cursor to it and press
[ENTER ] to deactivate it. (No information is lost; you
can always go back and reactivate any plot.) To verify that you have
deactivated the plot, cursor away from it and check that it’s not
highlighted.

(Sometimes you might want to graph more than one function on the same axis. In this case, make sure to deactivate all the functions you don’t want to graph.)  Now check the lines starting with Y1= ,
Y2= , and so on. If any
= sign is highlighted, either delete the whole equation
or deactivate it but leave it in memory. To delete an equation, cursor
to it and press the [CLEAR ] button. To deactivate it without
deleting it,
cursor to its = sign and press [ENTER ].
My screen looked like this after I deactivated all old plots and functions. 
Step 2: Enter the function.
If your function is not already in y= form, use
algebra to transform it before proceeding.
Two cautions:

Cursor to one of the Y= lines, press
[CLEAR ] if necessary, and enter the function.

Check your function and correct any mistakes.
For example, if you see a star * in place of an X , you
accidentally used the times key instead of [x,T,θ,n ].

Use the [◄ ] key and overtype any mistakes.
To delete any extra characters, press [ DEL ].
If you need to insert characters, locate yellow INS above
the [DEL ] key. Press [2nd DEL makes INS ] and type
the additional characters. As soon as you use a cursor key, the TI83/84
goes back to overtype mode.

Step 3: Display the graph.
“Zoom Standard” is usually a good starting point. It selects standard parameters of 10 to +10 for x and y.  Press [ZOOM ] [6 ].

If you don’t see your function graph anywhere, your window is probably restricted to a region of the xy plane the graph just doesn’t happen to go through. Depending on the function, one of these techniques will work:
ZoomFit
is a good first try.
Press [ZOOM
] [0
]. (Thanks to Marilyn Webb for this
suggestion.)
You can try to zoom out (like going
higher to see more of the xy plane) by pressing
[ZOOM
] [3
] [ENTER
].
Finally, you can directly adjust the window to select a specific region.
For other problems, please see TI83/84 Troubleshooting.
You can make lots of adjustments to improve your view of the function graph.
The window is your field of view into the xy plane, and there are two main ways to adjust it. This section talks about zooming, which is easy and covers most situations. The next section talks about manually adjusting the window parameters for complete flexibility.
Here’s a summary of the zooming techniques you’re likely to use:
You’ve already met standard zoom, which is
[ZOOM
] [6
]. It’s a good starting point for
most graphs.
You’ve also met zoom fit, which is
[ZOOM
] [0
]. It slides the view field up or
down to bring the function graph into view, and it may also stretch
or shrink the graph vertically.
To zoom out, getting a larger field of view with less detail, press
[ZOOM
] [3
] [ENTER
].
You’ll see the graph again,
with a blinking zoom cursor. You can press
[ENTER
] again to zoom out even further.
To zoom in, focusing in on a part of the graph with
more detail, press [ZOOM
] [2
] but don’t
press [ENTER
] yet. The graph redisplays with a blinking
zoom cursor in the middle of the screen. Use the arrow keys
to move the zoom cursor to the part of the graph you want to focus on,
and then press [ENTER
]. After the graph redisplays, you
still have a blinking zoom cursor and you can move it again and press
[ENTER
] for even more detail.
Your viewing window is rectangular, not square.
When your x and y axes have the same numerical settings
the graph is actually stretched by 50% horizontally.
If you want a plot where the
x and y axes are to the same scale, press
[ZOOM
] [5
] for square zoom.
There are still more variations on zooming. Some long winter evening, you can read about them in the manual.
You may want to adjust the window parameters to see more of the
graph, to focus in on just one part, or to get more or fewer tick
marks. If so, press [WINDOW
].
Xmin
and Xmax
are the left and right
edges of the window.Xscl
controls the spacing of tick
marks on the x axis. For instance, Xscl=2
puts
tick marks every 2 units on the x axis. A bigger
Xscl
spaces the tick marks farther apart, and a smaller
Xscl
places them closer together.Ymin
and Ymax
are the
bottom and top edges of the window.Yscl
spaces the
tick marks on the y axis.If you want to blow up a part of the graph for a more detailed
view,
increase Xmin
or Ymin
or both,
or reduce Xmax
or Ymax
. Then press
[GRAPH
].
If you want to see more of the xy plane, compressed to a
smaller scale, reduce Xmin
and/or Ymin
,
or increase Xmax
or Ymax
. Then press
[GRAPH
].
Many of the graph windows shown in your textbook will have small
numbers printed at the four edges. If you want to make your graphing window look
like the one in the textbook, press use the numbers at left and right
edges for Xmin
and Xmax
, the number at
the bottom edge for Ymin
, and the number at the top edge
for Ymax
.
The grid is the dots over the whole window that line up to the tick marks on the axes, kind of like graph paper. The grid helps you see the coordinates of points on the graph.
If you see a lot of horizontal lines running
across the graph, your Xscl
is way too
small, and the tick marks are running together in lines.
Similarly, Yscl
is the number of y units between
tick marks. A bunch of vertical lines means your Yscl
is too small. Press [WINDOW
] and fix either of these
problems.
To turn the grid on or off: 
Locate yellow FORMAT above the [ZOOM ]
key. Press [2nd ZOOM makes FORMAT ].
Cursor to the desired GridOn or
GridOff setting, and press [ENTER ] to lock
it in.
Then press [ GRAPH ] to return to your graph.

First off, just look at the shape of the graph. A vertical asymptote should stick out like a sore thumb, such as x = 3 with this function. (Confirm vertical asymptotes by checking the function definition. Putting x = 3 in the function definition makes the denominator equal zero, which tells you that you have an asymptote.)
The domain certainly excludes any x values where there are vertical asymptotes. But additional values may also be excluded, even if they’re not so obvious. For instance, the graph of f(x) = (x³+1)/(x+1) looks like a simple parabola, but the domain does not include x = −1.
Horizontal asymptotes are usually obvious. But sometimes an apparent asymptote really isn’t one, just looks like it because your field of view is too small or too large. Always do some algebra work to confirm the asymptotes. This function seems to have y = 1 as a horizontal asymptote as x gets very small or very large, and in fact from the function definition you can see that that’s true.
While displaying your graph, press [TRACE
] and then
the x value you’re interested in. The TI83/84 will move the
cursor to that point on the graph, and will display the corresponding
y value at the bottom.
The x value must be within the current viewing
window. If you get the message ERR:INVALID
, press
[1
] for Quit
. Then
adjust your viewing window and try again.
You can trace along the graph to find any intercept. The intercepts of a graph are where it crosses or touches an axis:
x intercept  where graph crosses or touches x axis  because y = 0 
y intercept  where graph crosses or touches y axis  because x = 0 
Most often it’s the x intercepts you’re interested in, because the x intercepts of the graph y = f(x) are the solutions to the equation f(x) = 0, also known as the zeroes of the function.
To find x intercepts:
You could naïvely press [TRACE
] and cursor left and
right, zooming in to make a closer approximation.
But it’s much easier to make the TI83/84 find the intercept for you.
Locate an x intercept by eye. For instance, this graph seems to have an x intercept somewhere between x = −3 and x = −1.  Locate yellow CALC above the [TRACE ]
key. Press [2nd TRACE makes CALC ] [2 ]. (You select
2:zero because the x intercepts are zeroes
of the function.)

Enter the left and right bounds. 
[() ] 3 [ENTER ] [() ] 1 [ENTER ]
There’s no need to make a guess; just press [ ENTER ]
again.

Two cautions with x intercepts:
Finding the y intercept is even easier:
press [TRACE
] 0 and read off the y intercept.
This y intercept looks like it’s about −2/3, and by plugging x = 0 in the function definition you see that the intercept is exactly −2/3.
You can plot multiple functions on the same screen. Simply press
[Y=
] and enter the second function next to
Y2=
. Press [GRAPH
] to see the two graphs
together.
To select which function to trace along, press
[▲
] or [▼
]. The upper left corner
shows which function you’re tracing.
When you graph multiple functions on the same set of axes, you can have the TI83/84 tell you where the graphs intersect. This is equivalent to solving a system of equations graphically.
The naïve approach is to trace along one graph until it crosses the other, but again you can do better. We’ll illustrate by finding the intersections of y =(6/5)x−8 with the function we’ve already graphed.
Graph both functions on the same set of axes. Zoom out if
necessary to find all solutions.

Press [2nd TRACE makes CALC ] [5 ].
You’ll be prompted First curve? If necessary,
press [▲ ] or [▼ ] to select one of
the curves you’re interested in. Press [ENTER ].
You’ll be prompted Second curve? If necessary,
press [▲ ] or [▼ ] to select the
other curve you’re interested in. Press [ENTER ].

Eyeball an approximate solution. For instance, in this graph there seems to be a solution around x = 2. 
When prompted Guess? , enter your guess. In this
case, since your guess is 2 you should press 2 [ENTER ].

Repeat for any other solutions. 
As always, you should confirm apparent solutions by substituting in both equations. The TI83/84 uses a method of successive approximations, which may create an ugly decimal when in fact there’s an exact solution as a fraction or radical.
Updates and new info: https://BrownMath.com/ti83/