USING THE TI-83+ TO GRAPH AND ANALYZE FUNCTIONS
The keys we will be using are circled in the graphic below
Turns the Device ON and also
OFF while pressed after pressing the
key.
The
key acts as a shift key to
allow access to the commands in
yellow above many of the keys.
These keys
in the top row allow for graphing and
graph analysis, as well as modifying
our graph window. Note they are
smaller than the other keys on the
calculator.
is a key for entering variables in
our functions.
The
key essentially tells the
calculator “Yes, do what I just told you
to do.”
are our arrow keys for
controlling the cursor or moving along
our graph. Just below that set of keys
is the
key which clears screens,
equations, etc…
Now, let’s graph a “simple” set of functions.
First press the
key. You will then see the following window.
If there are currently equations entered in the calculator arrow
down to each line with an equation and press the
key.
Once you have a nice clear screen enter an equation.
For example let’s graph Y1 = X2 or as it looks on the calculator Y1 = X^2
We press the following buttons with our cursor next to “Y1 = ”
and then press
. This will produce the following screen:
Pressing the
key should show this graph
If you see something different you should press the
key to set your window
to these parameters:
Important Note:
is not the same as
.
denotes a negative
number (the sign is raised slightly) while
is used in equations and
calculations as a subtraction sign. Example:
are not the same.
The second denotes a negative 2.
After resetting the parameters, press
Now you should see the following.
again to see your graph.
If yours still doesn’t look like this (maybe you are missing axes)
Press
FORMAT
to view these options
this what we
want for now.
They mean (in order):
Rectangular Coordinates or Polar Coordinates (we want Rectangular)
Coordinates On or Coordinates Off (we want them on)
Grid Off or Grid On (creates a grid on the graph – we want them off)
Axes Shown or Axes Hidden (shows axes or not)
Labels Off or Labels On (shows x and y labels – either is fine)
Expression Off or Expression On (we want them on)
There are several things we can do now with this graph. We can zoom in various
parts of it to get a closer look, we can trace along and find specific values, we
can find where it’s zero points are (or where it meets the x axis), we can calculate
specific values for Y using X values.
Let’s start by zooming in. Press
to get this set of options
ZBox will let us choose a specific boxed area to zoom in on.
Zoom In will let us choose a center point with a cursor and by pressing ENTER
will zoom in centered around that point. Zoom Out expands the view of the
graph. ZDecimal, Zsquare, ZStandard (the default), ZTrig, and ZInteger all
Zoom to specific preset values of the calculator. Try them out to see what they
look like. ZoomStat is used solely for looking at values entered in lists and
Zoomfit calculates to show the minimum and maximum Y values to fit in the
screen.
Examples are shown here for a few of them that are useful to our function:
Fit
Box
Now let’s look a little more at our graph. Let’s trace the path of the function. Up
till now if we moved our cursor around the screen with our arrow keys we’d see X
and Y values for areas on the screen. We want to look at specific X and Y
values on our graph.
To do this we press TRACE
and that let’s us trace out the path of the
function and view specific X and Y values shown in the following images.
Well, that’s great but what if we want to know an exact Y value for any X?
We press
then
to see the next window of options.
This is the Calculate menu. We want 1:value so we choose it and
press the ENTER key. In this case we’ll find the value of Y when X is -2.
The cursor moves to X = -2 and Y = 4.
Try it out with several other X values
Now, we will look at our graph to determine just where our function meets or
crosses the X axis thus providing zero value. In other words Y=0 for a particular
X.
We press
then
to see the next window of options.
we want 2:zero so we choose it and press the ENTER key.
The calculator asks for the Left Bound of our guess
&
Then, the Right Bound of our guess
&
Then, it asks for an approximate location or our guess
&
Finally, we can view our zero
Next, let’s look at the relationship between 2 different graphs. Let’s add a
second graph. Press
and enter Y2 = 2 * X as shown here
Then press
again to see our two graphs
Looks a little cluttered so let’s
into a Box around an
interesting area.
That looks good.
Now, we can determine where these graphs intersect by using
TRACE or
2nd CALC. Try
and use your Up and Down arrow keys to hop
from graph to graph and the Left and Right keys to move along each graph.
Or, try the following for an exact measure of the intersection of our two graphs.
Press
and choose 5:intersect.
Select the First Curve (Function)
&
Then the Second Curve (Function)
&
Take a Guess
&
Now, you’ll view the Intersection of the two functions
You may want to practice with several other interesting functions some include
the following
Compare:
Take a look at:
Y = X^3
Y = sin(X)
Y = 3^X
Y = 2*sin(X)
Y = 3*X
Y = sin(2*X)
Where do they intersect?
Y = cos(X)
Which one “grows” the fastest?
Y = 2*cos(X)
The slowest?
Y = cos(2*X)
Among other variations
One final note about graphing with the TI-83. A feature which is not utilized by
many people nearly as much as it should be is the “Split screen” mode. Many
times it may be helpful to see two aspects of the function you are analyzing.
Pressing MODE
presents the menu below Choosing G  T gives you a
tabular and graphical view of your function while choosing Horiz presents a
graphical view and the functions themselves that can be dynamically edited.
GT
Horiz
The advantage to this is that students can now explain what is happening,
numerically, by a table, and graphically all valued ways to communicate math.