Texas Instruments TI-83 User manual

TI-83 Graphing Calculator Manual to Accompany
Precalculus Graphing and Data Analysis
How to Use This Manual
This manual is meant to provide users of the text with the keystrokes necessary to
obtain the output provided by the TI-83 graphing calculator as that obtained in the text.
This manual by no means covers all of the features of this calculator.
In addition, once a particular feature is introduced, it will not be discussed again.
For example, graphing is introduced in Section 1.2, therefore, when graphing is again
required in Section 6.4, the keystrokes required are not reviewed and are assumed to be
known.
Introduction to the TI-83
Before learning how to use the TI83 as a graphing calculator, an introduction to
the TI83 as a scientific calculator may be worthwhile. In this introduction, basic
calculator skills will be discussed.
Turning the Calculator On and Off
The ON button is located in the
lower left hand corner of the keyboard. To
turn the calculator off, press the 2nd button
and then the ON button. Notice that all 2nd
functions are in yellow on the keyboard.
An Introduction to the TI83 Keyboard
If you look at the bottom portion of the TI83, you should recognize that it looks
similar to a standard scientific calculator. This portion of the calculator is enclosed in the
box shown on the calculator above.
ON button
2nd
Function

When treating the graphing calculator as a scientific calculator, we typically work
from the HOME screen. This simply means there are no menus on the screen. Below I
have the HOME screen labeled. Notice the blinking cursor. In order to get to the HOME
screen from anywhere within the calculator simply press 2nd QUIT (QUIT is a 2nd
function located directly to the right of the yellow 2nd button).
Let’s review the keys associated with a scientific calculator starting with the 4 basic
functions of addition, subtraction, multiplication and division. The four binary operations
are located on the right side of the keyboard (they are blue). The traditional “equal sign”
is replaced with ENTER. So, to perform the operation 4 + 5, simply type 4 + 5
and hit ENTER.
The TI-83 is aware of the order of operations, so to evaluate:
(
)
6*543 −simply type:
3(4-5*6)
and hit ENTER. Note the * is the symbol for multiplication. The parenthesis are the
buttons located above the 8 and 9.
HOME
screen

EXPONENTS
Exponents can be handled using either the 2 xbutton or the caret key (^). For example, to
evaluate 2 5simply type 5and then push the 2 xbutton and hit ENTER. To evaluate 4 5 ,
type 5 ^ 4 and hit ENTER. NOTE: The 2 xbutton may only be used to raise a
quantity to the 2nd power.
To compute the reciprocal of a number use the 1− xbutton. For example to compute 1 5−,
type 5 and then push the 1− xbutton. Alternatively, you could use the caret key with
the “negative” button.
Notice the TI-83 automatically puts the solution in decimal form. Should you want your
answer to be in a fraction, use the FRAC option under the MATH menu. For example, to
compute the reciprocal of 5 with the solution in fraction
form, type: 5 and then push the 1− xbutton, but instead of
hitting ENTER, press the MATH button and you see the
following menu:
2
xCaret (^)
1−
x
“Negative”
button
MATH
button

We wish to access option 1:Frac . Since this is the option currently highlighted, we
select it by pressing ENTER or pressing the number 1 on the keyboard. You should
obtain the following:
Press ENTER to see the result:
Suppose we computed the reciprocal of 5 without using the FRAC option as follows:
We then realize that we wanted our answer as a fraction. Rather than retyping the
previous command, we could simply access the MATH menu and select FRAC and
obtain the following:

The calculator automatically stores the most recent output in a memory locator call Ans.
So, the calculator will take the output in Ans and convert it to a fraction!
NOTE: Ans can also be retrieved using 2nd and the “negative” button.
RADICALS
You should see the square root ( ) as a 2nd function above the 2 x
button. So to compute 36 simply press 2nd then press the 2 xbutton, then 3 6 close
the parenthesis and press ENTER. To evaluate
radicals whose index is different than 2 we again go to
the MATH button. Notice options 4 and 5 are radicals:
So, to compute 481, type 4then select option 5 from the MATH menu, then type 81,
close the parenthesis and hit ENTER.
EXPONENTIALS AND LOGARITHMS
The LOG and LN buttons on the keyboard on located in the
bottom left portion of the keypad. Notice that x 10 and x eare
2nd functions above these keys. It’s fairly straightforward to use
these features.
LOG
LN

For example to compute log 3, simply press the LOG button followed by a 3 and a close
parenthesis and hit ENTER. To compute 4 e, press 2nd LN followed by 4 and hit
ENTER.
TRIGONOMETRIC FUNCTIONS
Notice the SIN, COS, and TAN functions. To
use these features, we need to know whether
our angle is in Degrees or Radians. Setting the
angle is done by pressing MODE.
After pressing the MODE button you should see the following:
Currently, the calculator is in radian mode. If we wish to change the calculator to degree
mode we use the arrows on the keyboard to move the blinking cursor down to highlight
Degree and then press ENTER. You should have the following:
SIN, COS,
TAN
MODE

To get back to the HOME screen press 2nd QUIT. Suppose we wish to evaluate: o 30sin ,
we press the SIN button then 3 0 ) and hit ENTER.
The inverse trigonometric functions are second functions above their corresponding
function. So, 1 sin −is a 2nd function of sin, etc.
OTHER FEATURES
If your HOME screen ever becomes too cluttered, we can clear it by using the CLEAR
button.
Another neat feature is the 2nd ENTER feature. Press 2nd ENTER a couple of times. You
should see that previous entries appear on the command line. The TI83 can remember
about the last 7 –10 commands entered!!! These commands can then be edited.
The remainder of the manual discusses features as they arise in the text.
1.2 Graphs of Equations
Example 3 Graphing an Equation on a Graphing Utility
Graph the equation 6 3 36
2
x y+ =
SOLUTION
Step 1: Done on page 15.
Step 2: To enter the expression y x= − +2 12
2into a TI-83. Press Y =

You should see the following on your screen:
The highlighted Plot1 means StatPlot is on.
To turn it off use the up arrow to put the
cursor on Plot1 and hit enter.
Move the cursor back down to Y1= and your
screen should look like this:
In Y1, type in the following order (consult the figure for the location of these buttons)
1. ( -)
2. 2
3. X,T,θ,n
4. x2
5. +
6. 1
7. 2
Y =

Your screen should have the following:
STEPS 3 and 4: To obtain a
graph with the standard
viewing window press
ZOOM and then select
option 6. Zstandard.
Immediately a graph should
start to appear on the
standard window.
STEP 5: To adjust the viewing window, press WINDOW. Use the arrows to move the
cursor to the values you wish to change. We wish to change Ymin to -12, so move the
cursor to Ymin and make its value -12. Press GRAPH and you should obtain the
following:
( -)
NOTE: This is not
the subtraction sign.
This button represents
the negative of a
number.
X,T,θ,n
x2
This squares the
quantity preceding it.

w
USING THE TABLE FEATURE
The table feature can be activated by pressing 2nd GRAPH. In order for the feature to
work, you must have at least one equation entered in the Y = menu. Before proceeding to
the table, I first want to introduce the TABLESET feature. This is activated by pressing
2nd WINDOW on your TI-83.
After pressing 2nd WINDOW, the following should appear.
I first want to direct your attention to the Independent variable (x-variable) setting.
Currently AUTO is highlighted. This means the calculator will automatically fill in a
table starting at x= 0 and increasing by values of 1. To see this concept we will
reproduce Table 2 on page 18. Let Y1= x2-4. Press 2nd WINDOW to access table setup
and change
TblStart to -3 to
obtain the
following.
TaBLeSET
TABLE
Independent
Variable

Now press 2nd GRAPH to obtain the following TABLE:
You can use the arrows to scroll around the TABLE. Notice that whatever quantity the
cursor lies on is displayed in the bottom row of the TABLE.
Let's go back to TableSetUp to see the affect of changing the independent variable to
ASK. Bring up TableSetUp and use the cursor to
highlight Ask under the independent variable. Now
press ENTER. Your screen should look as follows:
Now press 2nd GRAPH to display a TABLE. The TABLE should be empty. If it is not,
press delete with the cursor in the X-column until it is empty. Your screen should look as
follows:
Enter values of xinto the X-column and the corresponding yvalues get automatically
filled in. For example we could enter x= -2, 0, and 2 and obtain the following:

These are the intercepts of the graph of the equation!!
EXAMPLE 8 Using a Graphing Utility to Find Intercepts
Use a graphing utility to find the intercepts of the equation y= x3-8.
SOLUTION
Graph Y1= x3-8 using Xmin = -5, Xmax = 5, Xscl = 1, Ymin = -20, Ymax = 10,
Yscl = 5.
The VALUE feature on a TI-83 evaluates an equation for any value of xand locates the
corresponding ordered pair on the graph of the equation. Letting x= 0 allows us to find
the y-intercept of the graph of an equation.
After graphing the equation, press 2nd TRACE (this activates the CALC menu)
You should obtain the following on your screen:
CALC
menu

We want to select option 1: value. After selecting this option, we obtain the
following:
After the X= type 0 and press enter to obtain the following:
Thus, when x= 0, y= -8.
We can use the ZERO feature on a TI-83 to determine the x-intercepts of the graph of the
equation. Again, go to the CALC menu, but this time select option 2: ZERO.
The calculator asks for a LEFT BOUND -this is a value of xto the left of the x-intercept.
To establish the left bound use the left and right arrows to move the cursor until it is left
of the x-intercept you wish to approximate, then press ENTER.
x-intercept

Notice the arrow. This is telling you the calculator will look for an x-intercept to the right
of this value.
The calculator now wants a RIGHT BOUND -this is a value of xto the right of the
x-intercept. Use the left and right arrows to
move the cursor somewhere to the right of the
x-intercept you wish to approximate and press
ENTER. You obtain the following:
You now need to give the calculator an initial guess as to the value of the x-intercept.
This can be any x-coordinate you wish provided it is between the left and right bounds.
Move the cursor near the x-intercept and press ENTER. The calculator then thinks for a
while and provides a solution:
The x-intercept is 2. w
1.3 Solving Equations
EXAMPLE 1 Using ZERO (or ROOT) to Approximate Solutions of an
Equation
Simply follow the same procedures as were used in Example 8 from Section 1.2 w

EXAMPLE 2 Using INTERSECT to Approximate Solutions of an Equation
Find the solution(s) to the equation 3(x-2) = 5(x-1). Round answers to two decimal
places.
SOLUTION
Graph each side of the equation: Y1= 3(x-2); Y2= 5(x-1) using the viewing window
Xmin = -4, Xmax = 4, Xscl = 1, Ymin = -15, Ymax = 5, Yscl = 5.
To determine the solution, find the x-coordinate of the point of intersection. Select the
CALC menu (2nd TRACE). Select option 5: INTERSECT by either highlighting
INTERSECT or Pressing 5.
The calculator displays the following:
If you press the left or right arrow, you should notice the cursor TRACEing along Y1.
Move the cursor near the point of intersection of the two graphs and press ENTER.
The screen displays the following:

Again move the cursor near the point of intersection and press ENTER.
The screen now displays the following:
Simply press ENTER a third time and the screen displays the coordinates of the point of
intersection:
The solution to the equation is x= -0.5. w
33 Check: The calculator now has x= -0.5 automatically stored. To check the answer
type 3(x-2) on the home screen and press enter. Do the same for 5(x-1). You obtain
the following:
The solution checks. w
1.5 Solving Inequalities
Example 8 Solving Combined Inequalities
Solve the inequality -5 < 3x-2 < 1 and draw a graph to illustrate the solution.

SOLUTION
Graph Y1= -5, Y2= 3x-2, and Y3= 1 using the viewing window Xmin = -8, Xmax = 8,
Xscl = 1, Ymin = -8, Ymax = 4, Yscl = 1. We wish to find the point of intersection
between Y1and Y2and the point of intersection between Y2and Y3. We will first find
the point of intersection between Y1and Y2. After graphing all three equations, bring up
the CALC menu and select 5:
INTERSECT. When First Curve?
appears, the cursor should be on Y1.
Move the cursor near the point of
intersection and press ENTER.
After pressing ENTER, the cursor automatically jumps to Y2. Again, move the cursor
near the point of intersection.
Press ENTER a third time and you obtain the point of intersection as (-1, -5).
We now wish to find the point of intersection between Y2and Y3. Bring up the CALC
menu and select 5: INTERSECT. The first curve is on Y1, but we want it on Y2. This is
accomplished by pressing the down arrow. Move the cursor near the point of intersection
and press ENTER. The cursor jumps to Y3. Again, move the cursor near the point of
intersection and press ENTER. Press ENTER a third time to obtain your solution, (1, 1).
We know we are TRACEing
on Y1because of this!!

The graph of Y2is between the graphs of Y1and Y3for -1 < x< 1. w
EXAMPLE 9 Solving an Inequality Involving Absolute Value
Solve the inequality | x| < 4
SOLUTION
Graph Y1= | x| and Y2= 4. To graph Y1= | x|, enter the Y = menu. With the cursor in
Y1, press MATH.
You should see the following on your screen:
Press the right arrow to highlight NUM:
MATH

Select 1: abs( and the absolute value function will appear in Y1. NOTE: If abs(
appears on your home screen rather than in Y1, you forgot to press Y = !
You should have the following on your screen:
Press X, T, θ, nto put the variable xafter the abs( and finally press ). Hit ENTER.
In Y2, we put 4 to graph Y2= 4. Set the viewing window so Xmin = -6, Xmax = 6,
Xscl = 1, Ymin = 0, Ymax = 6, and Yscl = 1. Press graph and use INTERSECT twice to
obtain the solution -4 < x< 4 since the graph of Y1 is below the graph of Y2in this
interval. w
1.6 Lines
Square Screens
To get a square screen on the TI-83 press ZOOM and select option 5: ZSquare.
ZOOM

The calculator will automatically graph any equations entered in the Y = menu. A note
about ZSquare -it will square the viewing window that is established. You may need to
adjust the initial window setting before using ZSquare.
1.7 Scatter Diagrams; Linear Curve Fitting
Example 1 Drawing a Scatter Diagram
The data listed in Table 9 (see page77) represent the apparent temperature versus relative
humidity in a room whose actual temperature is 72oFahrenheit. Draw a scatter diagram
using a graphing calculator.
Solution
First press the STAT button.
On the screen you should see the following:
Select 1: Edit by either pressing ENTER or pressing 1.
You should now be in the data editor.
STAT