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To the student: Purpose of Lab 7
Current trends in teaching mathematics utilize the graphics calculator both for making arithmetic calculations easier and for allowing students to develop critical thinking skills by applying mathematics to real-life problems. Since graphics calculator skills are required for success in subsequent mathematics courses, learning these skills before enrolling in credit mathematics courses is very important.
Texas Instruments has a feature on their website that may be helpful to you.
It's free and can be viewed at http://education.ti.com/educationportal/sites/US/nonProductMulti/training_online_tutorials.html?bid=4
It's an online how to use your graphing calculator site. It's great for students that need
detailed step-by-step instructions on how to work their calculators! I hope it's helpful!
You will need to use this calculator on labs. You may use the calculator on all exams.
Note: The explanations in this lab refer to the TI-82 (TI-83) graphics calculator. Operations with other TI calculators are described only when they differ from those with the TI-82 (TI-83).
Directions:
GETTING ACQUAINTED WITH THE GRAPHICS CALCULATOR
Press the ON key. If the contrast of the screen display needs adjustment, press the 2nd key and then press and hold down the t (up arrow key) to increase the contrast or the u (down arrow) to decrease the contrast.
KEY FUNCTIONS
The primary use for each key on the calculator is the label written directly on the key. Most keys have a second or even a third function written above the key.
In order to utilize the second function of a key described by the blue lettering above it, press the light blue 2nd key before pressing the key.
Example: ON turns the calculator on.
2nd ON turns the calculator off, since <OFF> is the second function of the ON key.
Note: Anytime the 2nd key has been pressed, the cursor display is a blinking to indicate that the secondary function of the next key pressed is activated. (If you pressed the 2nd key in error, you may cancel it by pressing the 2nd key again.)
The 2nd key on the TI-83, 85, and 86 is yellow and the secondary function above each key is described with yellow lettering.
In order to utilize a letter of the alphabet described by the gray lettering above a key, press the gray ALPHA key before pressing the key.
Example: Press ALPHA PRGM . The screen displays the letter C.
Note: Anytime the ALPHA key has been pressed, the cursor display is a blinking [A] to indicate that the alpha function of the next key pressed is in effect. Cancel the alpha function effect by pressing the ALPHA key again.
The ALPHA key on the TI-83 is green and the alpha function above the key is described with green lettering.
The ALPHA key on the TI-85 and 86 is blue and the alpha function above the key is described with blue lettering.
SETTINGS
To check the settings of the calculator, press the MODE key. For now, the items on the left side of the MODE menu should be highlighted. To change these settings, use the arrow keys to move about the items on the menu. Then ENTER to select a setting. To exit the MODE menu, press CLEAR or press 2nd MODE , which is <QUIT>.
The <MODE> function on the TI-85 and 86 is accessed by pressing 2nd MORE . To exit the MODE menu, press CLEAR (You may also exit by pressing the EXIT key or 2nd EXIT, which is <QUIT>.).
ARITHMETIC OPERATIONS
Using the gray number keys and the operation keys (to the right of the number keys), you may perform arithmetic operations on the home screen of the graphics calculator.
| Be careful to enter negative numbers using the negative key ( – ) and to perform subtraction by using the minus key – . |
| Exponents are written by using the ^ key. (i.e. 24 is input as 2 ^ 4 .) The x2 key may be used if the exponent is 2. (i.e. Input 3 x2 to display 32.) |
| The calculator performs operations according to the order of operations rule: working from inside to outside for parentheses, with powers and roots evaluated first, multiplication and division next (from left to right), and finally, addition and subtraction (from left to right). |
| Insert parentheses where necessary to carry out operations in the proper order. (The ( and ) keys are above the number keys.) |
| After inputting expressions, check for errors. |
| Before pressing ENTER , corrections or additions may be made by moving the cursor with the arrow keys to the character you wish to change, then do any of the following to edit: |
a) type over the character,
b) delete the character (using the delete key DEL ), or
c) insert omitted data by using 2nd DEL to access insert <INS> .
| After pressing ENTER , press 2nd ENTER which is <ENTRY>. The previous expression is retrieved and can be edited to correct an error or to change data and perform another calculation. Consider the following examples: |
Example A: You mistakenly entered 3.567 instead of 3.467.
Move the cursor to the 5 and type over the correction 4.
Example B: You mistakenly entered 3.67 instead of 3.467.
Move the cursor to the 6, press 2nd DEL for <INS> , and then insert 4.
Example C: Find the perimeters of the following rectangles (P = 2L + 2W):
Rectangle 1: width = 4.75 cm.; length = 7.32 cm.
Input: 2 ( 7.32 ) + 2 ( 4.75 ) ENTER . Perimeter: 24.14 cm.
Rectangle 2: width = 6.98 cm.; length = 8.67 cm.
Use <ENTRY> to retrieve the previous expression.
Change the values for length and width to those for the second rectangle. Then ENTER .
Input: 2 ( 8.67 ) + 2 ( 6.98 ) ENTER . Perimeter: 31.3 cm.
Note: Multiplication in this example is indicated by using the parentheses. The times key X may also be used for this operation. The screen display corresponding to this key is "*". When the variable "x" is input, a different key is used. (Inputting variable expressions is discussed later.)
EVALUATING EXPRESSIONS
Example 1: Evaluate 
Consider the following input: 7 + 29 – 5 ¸ 6
Insert parentheses so that the calculator will evaluate correctly.
Recall that in the absence of grouping symbols, as the input is now written, division will be done first using the order of operations rule.
Correct input: 7 + ( 29 – 5 ) ¸ 6 ENTER
Correct answer: 11
Example 2: Evaluate 
Are parentheses required for correct input?
Correct input: ( 4 ^ 3 + 6 ) ¸ ( 2 ( (–) 7 ) )
Correct answer: –5
Use the negative key ( – ) for inputting a negative number.
Important: When inputting an expression which contains a fraction, enclose the numerator and/or denominator of the fraction in parentheses if either contains expressions involving operations between numbers. Multiple parentheses are sometimes necessary since the calculator does not recognize brackets or braces as grouping symbols.
Example 3: Evaluate 
Input: ( 2nd x– 1 ( 5 – 8 ) ) ÷ ( 3 X 9 ) ENTER
Absolute value <ABS> is the second function of the x– 1 key on the TI-82.
Absolute value <ABS> is in the MATH menu on the TI-83. Press MATH . Then use the right arrow to move to NUM. Now press ENTER or 1 to select abs ( .
Using parentheses correctly:
| Parentheses must enclose ( 5 – 8) so that the absolute value of the difference of 5 and 8 is calculated. (Without the parentheses, the calculator will find the absolute value of 5 and then subtract 8.) |
| A set of parentheses must enclose the numerator and another set must enclose the denominator to ensure that the operations in each are performed before the division indicated by the fraction bar. |
Answer: .1111111111
The calculator will display only 10 digits of an answer on the TI-82 and 83 (12 on the TI-85 and 86). The answer above may be a terminating or repeating decimal (representing a rational number) which can be represented in fraction form. By using the fraction conversion function on the calculator 4 Frac, the decimal form of a rational number can be changed into its fraction form.
For the TI-82 and 83, 4 Frac is found in the MATH menu. While the answer to the problem above is still on the screen, press the MATH key. Highlight 4 Frac on the menu and press ENTER (or press the number 1). The screen displays
Ans4 Frac (indicating "answer to fraction"). Now press ENTER .
Ans4 Frac = 1/9
Since Ans4 Frac converts the decimal to the fraction 1/9, the answer to the problem is the rational number .111… in decimal form or 1/9 in fraction form.
TI-85, 86
<ABS> and 4 Frac are in the MATH menu. Please see the Appendix for details.
Example 4: Reduce to lowest terms 
If a fraction is not in lowest terms, the 4 Frac function can be used to reduce it to lowest terms.
Input: 629 ÷ 8514 Frac ENTER Reduced form: 17/23
Note: If a fraction is not reducible, the answer will be the same as the input.
Example 5: a) Simplify (379,000) (460,000) .
Input: 379,000 x 460,000 ENTER
Display: 1.7434E11
Very large or very small numbers are expressed in scientific notation on the calculator.
1.7434E11 = 1.7434 x 1011
= 174,340,000,000 Answer in normal form
b) Simplify (.000379) (.000046) .
Input: .000379 x .000046 ENTER
Display: 1.7434E–8
1.7434E – 8 = 1.7434 x 10 – 8 = .000000017434 Answer in normal form
Example 6: Evaluate 
.
Input: 2nd x2 ( 496 + 391 ) ENTER
Answer: 29.78254522
The square root Ö is the second function of the squaring key x2 . Parentheses are required for the expression under the Ö when there are operations to be performed between the numbers.
EVALUATING EXPRESSIONS FOR A SPECIFIED VALUE OF THE VARIABLE
TI calculators offer several methods of evaluating an expression or formula for specified values of the variables. Only two of those methods will be discussed here: 1) directly substituting values for the variables on screen and 2) storing values for the variables in memory locations corresponding to letters on the calculator. Examples follow.
Example 7: Evaluate x4 + 5x3 – 2x2 – 5x for x = – 2.
Method 1: Direct substitution
Replace each x with – 2 as you input the expression.
Input:
( (–) 2 ) ^ 4 + 5 ( (–) 2 ) ^ 3 – 2 ( (–) 2 ) ^ 2 – 5 ( (–) 2 ) ENTER
Answer: –22
Parentheses are required when raising a negative number to a power.
Method 2: Storing values for the variables
The same expression can be evaluated for x = –2 by storing –2 in the memory location for X on the calculator. To store a numeric value in the memory location of a letter, use the STO4 key.
Store the number value –2 in the memory location for the letter X.
Input: –2 STO4 X,T,q ENTER
The X,T,q key is a direct way to access the letter X on the TI-82 ( X,T,q ,n on the TI-83). (Note that the letters on the TI-82 and 83 are capitals.)
Since X is the ALPHA function of the STO4 key, –2 may also be assigned to the letter X in the following manner:
Input: –2 STO4 ALPHA STO4 ENTER
Now to evaluate x4 + 5x3 – 2x2 – 5x for x = –2, input the expression as follows:
Input: X,T,q ^ 4 + 5 X,T,q ^ 3 – 2 X,T,q ^ 2 – 5 X,T,q
ENTER Answer: –22
See the Appendix for details on the use of the STO4 key and the use of letters which represent variables.
GRAPHING
The graphing function keys are located directly below the screen on the TI-82 and 83 calculators.
TI-85, 86 The GRAPH menu on the TI-85 and 86 is accessed through the GRAPH key. Then the F keys are used to select items from the menu. See the manual for details.
In order to graph an equation (function) in x and y, first solve the equation for y. Press the Y= key. The screen display shows a blinking cursor at Y1 = where the equation rule may be input. (Any equation which is already entered on that line can be erased by pressing CLEAR .) As many as 10 equations may be entered for graphing. The calculator will graph the equations entered sequentially.* If you wish to "turn off" the graph of any of the equations entered, place the cursor on top of the "=" and press ENTER . Reversing the process turns the graph back on. If the "=" is highlighted, the graph is activated.
*This setting is controlled by the MODE menu which was discussed on the first page of this lab.
Example 8: Graph 
.
The equation is already solved for y. Input " x – 1" for Y1.
Press Y= . Input: ( 2 ¸ 3 ) X,T,q – 1.
(Note that parentheses are required when multiplying a fraction times a variable.)
Press GRAPH to display the graph of the equation.
Press the WINDOW key to display the dimensions of the rectangular viewing window for the graph. The viewing window is determined by six values:
Xminthe lowest x-value on the screen display, Xmaxthe highest x-value on the screen display, Xsclthe space between tick marks on the x-axis, Yminthe lowest y-value on the screen display, Ymaxthe highest y-value on the screen display, Ysclthe space between tick marks on the y-axis.
The window settings displayed represent the "standard viewing window." Settings for the standard viewing window are –10 to 10 on each axis, with tick marks 1 unit apart. These are the settings for the graph above.
The window settings may be changed manually by using the arrow keys to move about the menu. Changes may be made by typing over, deleting, and/or inserting as needed. Preset viewing windows may be selected from the ZOOM menu. (See below.)
The FORMAT settings affect the graph display also. Press the WINDOW key. Then use the right arrow to move to FORMAT. (For the TI-83, 2nd ZOOM is <FORMAT>.) On the FORMAT menu, all items to the left should be highlighted at this time. To change settings, move through the menu with the arrow keys and press
ENTER to highlight the selected items.
Press the ZOOM key to access the ZOOM menu which offers several options for changing the viewing window quickly. (See the calculator manual for complete details of the features of the ZOOM menu.) The standard viewing window can be easily set from the ZOOM menu.
Select 6:ZStandard from the menu by pressing 6 or by using the down arrow to highlight the selection and pressing ENTER . The graph immediately appears on screen in the standard viewing window (dimensions of –10 to 10 on each axis, with tic marks 1 unit apart).
While a graph is displayed on screen, the coordinates of points on a graph can be observed by using the TRACE function.
Press TRACE . A blinking cursor appears on the graph. The x and y coordinates at the bottom of the screen indicate the coordinates of the cursor’s position on the graph. By using the left and right arrows, you may trace along the graph, with the x and y values for each new position of the cursor displayed on the screen.
If you move the cursor to the right or left beyond the current window setting, the cursor continues to trace the path of the graph. The viewing window settings change horizontally, but not vertically. If you wish to view the position of the cursor, you may change the vertical window settings (Ymin and Ymax) manually. (Note: The numeral 1 in the upper right hand corner of the screen refers to the number of the function (Y1) which the cursor is tracing.)
Example 9: Find the x-intercept for the graph above. (Recall: The x-intercept is where the graph crosses the x-axis.)
Press TRACE and move the cursor to the apparent x-intercept. In the display shown here, x = 1.4893617 and y = – .0070922. To observe a more detailed view of the x-intercept, use the Zoom In function.
Zoom In to isolate a point in a small viewing window with the cursor at its center.
With the cursor on the apparent x-intercept, press ZOOM . Now select 2: Zoom In and press ENTER .
If the cursor appears to be on the x-intercept, read the x-coordinate from graph. (The y-value should be 0, or very close to it.)
For a closer look, press TRACE and adjust the cursor, if necessary, to move to the x-intercept.* Then press ZOOM [2] and ENTER again to Zoom In closer. Repeat this procedure if you desire to estimate the x-intercept as accurately as possible. The x-intercept here seems to be approximately 1.5.
* Pressing TRACE first keeps the cursor on the graph. However, you may adjust the cursor by using the arrow keys, without pressing TRACE . For example, if the y-value is already 0, simply use the right or left arrow to adjust the cursor before zooming in again.
The x and y-values for equations input in the Y= menu may be viewed by using the <TABLE> function on the TI-82, 83, and 86 calculators. The TABLE functions on the TI-82 and 83 are very similar. <TABLE> is the second function of the GRAPH key on both calculators.
Press 2nd GRAPH . Use the up or down arrows to scroll through the table of values for any equation which is currently assigned to a function in the Y= menu.
The TI-85 is not equipped with a TABLE function. However, a TABLE program is available and may be downloaded to your calculator.
is the second function of the WINDOW key on TI-82 and 83 calculators.. Press 2nd WINDOW . From this menu, you can set TblMin (TblStart on the 83) and D Tbl.TABLE SETUP <TblSet>
TblMin sets the lowest x-value on the screen when the <TABLE> appears. (Other values may be displayed by scrolling with the up and down arrows.) D Tbl sets the increments between successive x-values. For the display at right, TblMin is set at 0 and D Tbl is set at 1.
Press 2nd WINDOW to access <TblSet>. Now set the TblMin to 0 and D Tbl to .5.
Press 2nd GRAPH to display the <TABLE>.
Notice that the beginning x-value is 0 and the increment between successive x-values is .5.
Note that an x-value of 1.5 corresponds to a y-value of 0. Therefore, the x-intercept estimated from the graph is confirmed by examining the table.
<TblSet> also allows you to select whether you want the calculator to fill in the table values automatically Auto or to wait until you Ask. (The default setting is Auto.)
See complete details for all calculator functions in the manual.
Press ZOOM and then 6 to display the graphs in the standard viewing window.
Press TRACE . Move the cursor to the point of intersection to determine the coordinates.
To examine the point of intersection more closely, you may use Zoom In (used in Example 12 to find the x-intercepts). However, a different method for finding the point of intersection is demonstrated here: the calculator’s Intersect function which is accessed from the Calculate menu.
While the graphs are displayed on the screen, press 2nd
TRACE to access <CALC>. Select 5: Intersect from the menu.
The cursor appears on the graph of Y1 at the center of the screen. (Note the number 1 in the upper right corner of the screen.) Move the cursor with the right arrow along this graph to the point of intersection. Press ENTER to mark the apparent point of intersection on the "First Curve".
Now the cursor moves to the graph of Y2. (Note the number 2 in the upper right corner of the screen.) Adjust the cursor if necessary. Then press ENTER to mark the apparent point of intersection on the "Second Curve".
Now press ENTER to "Guess" the point of intersection. The x and y coordinates of the point of intersection appear on screen.
The point of intersection for the equations appears to be x = 3 and y = 5 or the ordered pair (3, 5).
See your calculator manual for utilizing other functions on the Calculate menu for the TI-82 and 83.
Important: The purpose of this lab is to learn the calculator skills necessary to succeed in future math courses. Use a graphics calculator to work these exercises. Examples in this lab provide detailed instructions for the calculator skills required for these exercises.
For problems 1 – 5, simplify. Write answers in decimal and fraction form when applicable. If answers on the calculator are given in scientific notation, write them in normal form.
1. 
2. 
3. 
4. 
5 a) – 34
b) (– 3)4
6. a) (442,000) (78,000)
b) (.000083) (.00327)
7. Reduce to lowest terms:
8. Evaluate: 2x5 – 9x4 + 5x2 – 13x – 28
a) for x = – 3;
b) for x = 2.76.
10. Estimate the x and y-intercepts from the graph of the equation in problem 9.
x-intercept ______________
y-intercept ______________
Copyright 1999, Collin County Community College and Rosemary M. Karr, Ph.D. All material on this site is for CCCC class use only. Any unauthorized duplication or distribution is prohibited.
