NAME ______________________
DIRECTIONS: Answer each question INDIVIDUALLY.
All questions should be directed to Ms. Watson.
Academic Year 2000-2001
Level III - Handout - Point Value: 50 points
[Y=] key
The [Y=] key is the central key used when graphing functions using a
calculator. This is the window where you can enter up to ten functions
into the TI-83 calculator, Y1, Y2, Y3, … Y9, Y0. (Use the [down-arrow]
key to see the other three lines to enter functions.) If you enter more
than one function at a time, the calculator will graph all the function in
which the "=" sign is highlighted. For example, in the window to the
right, Y1, Y3, and Y4 will be graphed only. When entering a function,
you will use the [X,T,,n] key for the variable, which in most cases is
the letter "X".
Enter the given functions and view one at a time by using [Zoom] key and
[6:ZStandard]. Draw a sketch of your viewing window for each question.
1. y  3x  2
2. y  x2
3. y  x
4. y  x
5. y  x3
6. y  3 x
7. y 
1
x
 1
10. y   
3
8. y 
1
x2
x
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9. y  2x
Academic Year 2000-2001
11. You have just graphed our ten "basic" functions. Go back and label the "important"
points and draw and label the asymptotes using a different color pen.
12. Based on your previous answers, how did the calculator indicate to you that there is
an asymptote? (It doesn't draw dashed lines for you.)
Why doesn't the calculator draw dashed lines? To graph a function, the calculator just plots
points and connects them. It doesn't think. You must do the thinking for the calculator.
13. Sketch the given functions based on what the calculator shows you, i.e. interpret
the calculator screen (don't just copy it).
3x  5
a. y  2
b. y  x3  x 2  3x  2
c. y  4  3 x  1
x 4
Different Graphing Options
There are 7 different options for the calculator to graph functions.
Notice the different symbols to the left of the equation names in the
window shown to the right. They were changed by placing the blinking
cursor on top of the given symbol and hitting [ENTER].
Change your [Y=] window as shown in the picture.
14. Write a particular linear function here _____________ and enter the function into
each equation line Y1 through Y7.
15. Graph each Y1 through Y7 one at a time. Describe the different graphing options.
Y1 option: _________________________________________
Y2 option: _________________________________________
Y3 option: _________________________________________
Y4 option: _________________________________________
Y5 option: _________________________________________
Y6 option: _________________________________________
Y7 option: _________________________________________
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Academic Year 2000-2001
[Window] key
The [Window] key displays the current settings of the viewing
rectangle. After graphing with the [6:Zstandard] option, you should see
the window to the right. [Xmin,Xmax] tells you the interval of the
displayed x-axis. [Ymin,Ymax] tells you the interval of the displayed yaxis. Xscl and Yscl determine where tick marks are placed on the xaxis and y-axis. You can manually change the intervals and
placement of the tick marks to suit your needs.
Adjust the window settings so that the function appears on the viewing rectangle
and you can see the important behavior. Record your settings. Note: You will
need to use your graphing technique knowledge.
16. y  x  15  20
Xmin =
Xmax =
Xscl =
Ymin =
Ymax =
Xscl =
19. y  60  12x  7x2
Xmin =
Xmax =
Xscl =
Ymin =
Ymax =
Xscl =
17. y 
3
 24
x  10
18. y  90  9.8x
Xmin =
Xmax =
Xscl =
Ymin =
Ymax =
Yscl =
20. y  20x  4
Xmin =
Xmax =
Xscl =
Ymin =
Ymax =
Yscl =
21. y  40  3 x  8
Xmin =
Xmax =
Xscl =
Ymin =
Ymax =
Yscl =
Xmin =
Xmax =
Xscl =
Ymin =
Ymax =
Yscl =
[Zoom] key
The [ZOOM] key is used
to change the window
settings of the viewing
rectangle without directly
setting the parameters
using the [Window] key.
There are 10 different
options from which to
choose.
continues
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Academic Year 2000-2001
[1:ZBox]
This option allows you to choose a "boxed" area of your screen to use as your viewing
rectangle. To do this, first hit the [Zoom] key and [1:ZBox]. Using the arrow keys, place
the cursor on one corner of the "boxed" area you want, hit [Enter], move the cursor using
the arrow keys again (thus creating a box), and hit enter when you've created your
desired box.
[2:Zoom In]
This option will shrink the viewing rectangle. To do this, first hit the [Zoom] key and
[2:Zoom In]. Using the arrow keys, place the cursor where you would like the center of
the new screen and hit [Enter].
[3:Zoom Out]
This option will expand the viewing rectangle. To do this, first hit the [Zoom] key and
[3:Zoom Out]. Using the arrow keys, place the cursor where you would like the center of
the new screen and hit [Enter].
[4:ZDecimal]
This window changes the window setting to the following: Xmin=- 4.7, Xmax=4.7,
Ymin=-3.1, Ymax=3.1. Once nice feature about this option is that the pixels are then 0.1
unit. So, when you trace a graph, the x-coordinate is in increments of 0.1.
[5:ZSquare]
This option adjusts the window settings so that the increments in the x and y directions
are the same. Why? This will make a circle look like a circle.
22. Solve for y: x 2  y 2  25 (Equation of a circle with radius 5.)
Answer: ______________
23. You should have gotten two answers to problem 22. Did you? If not,
contact Ms. Watson to find out what you are not thinking about.
24. Enter the two equations into Y1 and Y2. First, graph using ZStandard and
draw your results below. Then graph using ZSquare and draw your
results below.
ZStandard
ZSquare
Notice, the Zsquare makes it look like a circle.
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Academic Year 2000-2001
[6:ZStandard]
This option produces the default window with the following settings: Xmin=-10,
Xmax=10, Ymin=-10, Ymax=10. This is usually the first window used unless you know
ahead of time that other settings will be best.
[7:ZTrig]
This option adjusts to a window typically appropriate for trigonometric function. The
settings are as follows: Xmin=-(47/24), Xmax=(47/24), Xscl=/2, Ymin=-4, Ymax=4,
Yscl=1.
[8:ZInteger]
This option adjusts the window so that the pixel size is 1 in both directions.
[9:ZoomStat]
This option adjusts the window so that all statistical data points are plotted.
[0:ZoomFit]
This option adjusts the window setting by changing the Ymax and Ymin only so that the
maximum(s) and minimum(s) are displayed. Be careful. If the maximum(s) and
minimum(s) are outside the current interval [Xmin,Xmax], they will not be displayed.
[Trace] key
Remember that the calculator plots points and connects the dots to
graph an equation? Well, by hitting the [Trace] key after you have
graphed a function, you can see the coordinates of those points
(x,y) at the bottom of the screen. Also notice the equation is shown
in the upper right hand corner. If you are graphing more than one
equation at a time, you use the [up-arrow] and [down-arrow] keys to
change the function you are tracing.
25. Graph y  x3  5x  2 using the appropriate zoom key to fill in the ycoordinate of the following points on the graph.
(-2.4, ____) (-1.6, ____) (0, ____) (1.2, ____) (3.1, ____)
Which zoom key did you use? ______________
[Graph] key
The [Graph] key will graph the selected equations using the current window settings.
[2nd] [Zoom] or yellow [Format] key
The yellow [Format] key allows you to change the mode settings for
graphing functions. Most of the time, we have all the settings on
the left highlighted. To change a setting, use the arrow keys to
move to a setting and hit [ENTER].
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Academic Year 2000-2001
Enter the function y   x  3   2 into your calculator and graph.
2
26. Change from "CoordOn" to "CoordOff". What's the difference?
27. Change from "GridOff" to "GridOn". What's the difference?
28. Change from "AxesOn" to "AxesOff". What's the difference?
29. Change from "LabelOff" to "LabelOn". What's the difference?
30. Change from "ExprOn" to "ExprOff". What's the difference?
[2nd] [Graph] or yellow [Table] key
The yellow [Table] key displays a table containing the x and y
coordinates of all entered equations in the [Y=] window. According to
the screen to the right, there are at least two equations entered, Y1
and Y2. This feature can be used when evaluating a function for many
different values, as shown next.
[2nd] [Window] or yellow [Tblset] key
The yellow [Tblset] key allows you to change the settings of the table
window. When "Indpnt" and "Depend" are set on "Auto", "TblStart" is
the first value of the table for the x variable and "Tbl" established
the increment of the x variable. With this setup, the table will
automatically display the x variable with its related function values.
There may be a time when you want to enter values for the x variable
of the functions listed in the [Y=] window. In order to do this, set
"Indpnt" on "Ask". Then when you view the table, you will be able to
enter any value for x you wish. See the windows below.
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Academic Year 2000-2001
Deleting in a Table
When "Indpnt" is set on "Ask", you may want to delete specific values of the x column of the table. To do
this, highlight the number you wish to delete and hit the "DEL" key.
Enter these functions into the calculator:
Y1  8x  2x 2  1; Y2  7  3x ; Y3  3 ; Y4  7  5x
31. Evaluate the following functions using the table feature of the calculator.
 1
c. Y1   ______
3
a. Y1 2  ______
b. Y1 0  ______
d. Y2  4  ______
e. Y2  3  ______

f. Y2  4  ______
g. Y3  1  ______
h. Y3 1500   ______
i. Y3  3   ______
j. Y4 0   ______
k. Y4 1  ______
l. Y4  2  ______

[VARS] key
The [VARS] key is another way to evaluate functions that are entered into the [Y=] window. The TI-83
uses standard function notation such as Y1(2) on the Home screen. To do this, hit the [VARS] key, use
the [right-arrow] to go to the "Y-Vars" menu, choose [1:Function], choose Y1, and then enter "(2)". Hitting
enter will evaluate the Y1 function at 2. This may seem like a long process but remember that you can
bring up you last entry by hitting [2nd] [ENTER] or yellow [ENTRY]. As you do this step, you will see a lot
of other options along the way such as [4:Picture] , [5:Statisitics], [3:Polar]. Some of these will be
discussed at a later time.
Clear the [Y=] window. Enter these functions: Y1 
1
and Y2  5x  2 .
x
Y1(2)  Y1(3)
Y1(5)
1 1

2
3
33. Evaluate:
1
5
 1
35. Evaluate: 3  Y1 
3
34. Evaluate: 2  Y1 2   Y2  3  
37. Evaluate: Y2  Y1 3  
32. Evaluate:
36. Evaluate: Y1 Y2  3  
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