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ADVANCED FUNCTIONS and MODELING Updated 7-19-06
Ti-83, TI-83+, TI-83+ silver edition, TI-84+, TI-84+ silver edition
…reference cards for student notebooks, compliments of the North Carolina Early Mathematics Placement Testing Program.
Visit us at www.ncempt.org
To Get the Calculator Ready to Graph a Function or a Set of Data: a) Press b) At
Y=
and clear out all equations.
, if Plot 1, 2 , or 3 is highlighted, then press ENTER plot to deactivate.
on each highlighted
Y=
c) Press
ZOOM
d) Press
2nd
6
(standard screen).
ZOOM
(format) and be sure everything in the left column is
highlighted. e) Press
MODE
and be sure everything in the left column is highlighted.
f) For a statistics application: 1) To clear one list, press
STAT
1
(edit), cursor up to the top and
highlight the name of list you want to clear, then press 2) To clear all lists, press
2nd
(memory), then
+
CLEAR 4
ENTER
ENTER
.
.
3) If you lose an entire list, including the data, because you pressed DELETE instead of CLEAR, go to STAT
5
then go back to STAT
and your list will be there with the original
EDIT
(set-up editor), press
ENTER
,
data. To make suggestions OR to obtain a complimentary copy of the Word file for these cards, contact Ellen Hilgoe
NC EMPT Program Manager E-mail:
[email protected] NC EMPT is an outreach program of the UNC Office of the President
GRAPHS AND THEIR TABLES:
p. 2
What I want the calculator to do:
Which keystrokes it takes to do it:
1. To see a table of values from a graph:
a) Press Y=
a) Set the table to the starting value of my choice and to change in the increments of my choice.
Press
b) View the values in the table.
b) Press
2. To calculate the point of intersection of two graphs:
and enter the equation.
2nd
(table setup).
WINDOW
Enter the value where you want the table to start and arrow down to set the increment value ( Tbl). Leave the independent and dependent on Auto. 2nd
(table).
GRAPH
Press Y= , enter the equations, and graph. Use the zoom settings or window settings to be sure the intersection of the two graphs can be seen. Press
2nd
(Calc)
TRACE
(intersect). Then press
ENTER
5
three
times to find the coordinates of the intersection point.
3. To graph an absolute value function: Example:
y 3x 2 5
Press
Y=
ENTER
2nd
0
(catalog), then
(abs). Enter the expression
between the absolute value bars, close with would be keyed in this way on the calculator:
Y1 abs 3x 2 5
)
, and then type the remainder of the
equation. Now graph.
Note: An alternate method to access the absolute value function (abs) is to press MATH, NUM, ENTER.
4. To graph a piecewise function: x if x 2 Example: y 2 x if x 2 would be keyed in this way on the calculator:
Y1 x x 2 Y2 x
2
x 2
To type a less than or greater than symbol, go to nd 2 , MATH.
For the first piece, press
Y=
and
place the expression between parentheses followed immediately by placing the domain of that piece between parentheses. Repeat this pattern for the remaining pieces. Be sure to press MODE
and scroll down and highlight
“Dot” before graphing the function.
p. 3
5. To graph the inverse of a function:
Press
PRGM M
2nd
(Draw). Then
choose #8 (DrawInv), followed by an expression containing x or one of the functions in Then press
PRGM M
.
(not GRAPH). To clear
ENTER
the drawing of the inverse, press Note: The drawing of the inverse is overlaid on top of the Graph screen. It cannot be traced.
Y=
2nd
(Draw) and then chose #1 which is
(ClrDraw).
SCATTER PLOTS AND GRAPHS OF REGRESSION: What I want the calculator to do:
Which keystrokes it takes to do it:
6. To put data in the calculator:
Press
STAT
(edit) ,
1
ENTER
.
Then put data into the lists.
7. To create a user-friendly window: (This makes the trace feature have “nice” values).
Press
8
ZOOM
ENTER
integer values ZOOMOR press WINDOW
for and
set x-min to –5 and x-max to 4.4 or some multiples of these values. The y-max and y-min can be any values.
8. To change the window settings on the graphs:
Press
and then set the maximum
WINDOW
and minimum settings and the scale by which you wish to increment the axes OR use ZOOM
9
. .
ZOOM 9. To create a scatter plot with data in L1, L2:
Put the independent data into L1 and the dependent data into L2. Go to arrow up, highlight ENTER
. Press
(zoom stat).
PLOT 1 ZOOM
Y=
,
, and press 9
p. 4
10. To turn the diagnostics on so the calculator will compute r-values (correlation coefficients) or r 2 values when regressions are calculated:
2nd
(catalog), press x 1 o (for words beginning with the letter d), Press
0
then arrow down to DiagnosticOn. Then press twice.
ENTER
11. To calculate the regression equation with data in L1 and L2:
Press
STAT
.
ENTER
calculated, press
ENTER
Press
, press
Y=
1
. Finally, press
GRAPH . .
, arrow over to CALC
STAT
L3 will contain the residuals.
2nd
2nd
(L2)
2
,
(L1)
1 VARS
→
Y-VARS
(Y1).
ENTER
. Then your equation is in Y1.
STAT
1
Go to
1
(function)
1
(edit). Go to the top
of an empty list , such as L3. Highlight the L3. Type 2nd
L3 Y1 L1 when L1 contains the actual x values, and
,
then choose the type of regression from the
,
values of the data, L2 contains the actual
EQ
(RegEQ), and
choices listed. Then press
Note: A residual is the distance between the actual data value and the calculated data value.
VARS ,
for statistics, arrow over to
for equation, press
14. To calculate residuals for a regression with data in L1 and L2:
twice.
After the regression equation has been
press 5
13. An alternate method for steps #11 and #12 above.
,
then choose the type of regression from the choices listed. Then press
12 . To plot the regression line or curve on the scatter plot:
CALC
, arrow over to
Y-VARS
y(
2nd
2
(L2)
1
(function) 1
(L1)
VARS
)
1
(Y1) ENTER
p. 5
OTHER STATISTICAL GRAPHS: What I want the calculator to do: Enter the data into a list. Go to
15. To create a histogram for a set of univariate data:
(stat plot), press
Note: Begin by clearing out all equations in Y= AND by checking to see that stat plots are ON (see p.1).
2nd
Y=
and arrow down to
ENTER
Type. Use the right arrow to highlight the histogram, then press
. Make sure
ENTER
that the x-list is the one the data is in. 9
to graph. Press
ZOOM
and
WINDOW
adjust settings to integer values. Press TRACE
to get the numbers off the bars of
the histogram. 16. To create a box and whisker plot for a set of univariate data:
2nd
Enter the data into a list. Go to (stat plot), press
Y=
, and arrow down to
ENTER
Type. Use the right arrow to highlight ONE* of the box plots, then press
ENTER . . Make
sure the x-list is the one the data is in (you can change it by highlighting it and typing over the list name). Press Note: The first choice of box plots is a modifiedbox plot which shows outliers. The second box plot does not.
ZOOM
Press
9
to graph. You can
to get the minX, Q1, med,
TRACE
Q3, and maxX numbers off the box plot.
SEQUENCES: What I want the calculator to do:
Which keystrokes it takes to do it:
17. To find a particular (nth) term in an arithmetic sequence given the first term, u1 , and the common difference, d:
Enter the first term, u1 , then press
or to find a particular (nth) term in a geometric sequence given the first term, u1 , and the common ratio, r:
Press
2nd
(-)
(Ans)
+
ENTER .
and then
your d value for an arithmetic sequences OR press
2nd
(-)
(Ans)
x
and then
your r value for a geometric sequence. Continue pressing
ENTER
and count to
find the nth term of the sequence.
p. 6
18. To enter a sequence of values into a list: Note 1: If you want to see your formula every time you highlight the list, begin and end with quotation marks. Use
ALPHA
+
for quotes.
Example: “seq(X,X,1,3,.5)” Note 2: To clear out a formula, cursor to the top of the column and press CLEAR, ENTER, CLEAR, ENTER. Then to clear out all the data, cursor back up to the top and press CLEAR, ENTER again.
Go to STAT 2nd
(list),
STAT ,
X
(edit). Highlight L1. Press
1
X
,
,
OPS
, , enter beginning value of
sequence, , , enter ending value, increment,
)
(seq),
5
, then
,
, enter
ENTER . .
Example: seq(X,X,1,3,.5) Result: (1, 1.5, 2, 2.5, 3)
19. To enter a recursively defined formula for a sequence:
1) Press
MODE
, arrow down three lines,
highlight “Seq”, then 2) Press
ENTER
.
. For n Min, enter the position
Y=
number of the first term in the sequence. For u n , enter the recursive formula. To type 2nd
the letter u in the formula, press 7
. To type the variable n , press the
X,T, , n
key followed by a
For u n Min
1) Press
.
, enter the starting value
of the sequence. Then
20. To view the table of values of a recursively defined formula:
)
2nd
WINDOW
ENTER
.
(Table Setup).
The TblStart should match the n Min. The Tbl represents the scale factor to be used in the table. This is most commonly set at 1. Highlight “Auto” for both the independent and dependent variables. GRAPH 2) Press 2nd (Table) to find a list of the n and u n values. Arrow up or down the two columns to find the requested
values.
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TRIGONOMETRY: What I want the calculator to do:
Which keystrokes it takes to do it:
21. To change from degree to radian mode (or vice versa):
Press
choose the mode you prefer. Press ENTER Then type
22. To find the value of a trig function given the angle measure:
, arrow down two lines and
MODE
2nd
Quit
to clear the screen.
Put the calculator in degree or radian mode. Type the trig function (sin, cos, or tan) and then the angle value. Enclose with ENTER
23. To find the value of a reciprocal trig function given the angle measure:
a) To find csc x, type
c) To find cot x, type steps above).
, the angle
sin
26. To solve a trig equation:
x: 2cos x 3, for 0 x 360
Example: Solve for
Let
y1 2cos x
Let
y2 3
cos s tan s
x 1
,
ENTER
,… (repeat ,… (repeat
Put the calculator in degree or radian mode. Type 2nd the trig ratio,
sin Example: Show that tan cos Let y1 tan sin Let y2 cos
. Type
Put the calculator in degree or radian mode.
b) To find sec x, type steps above).
25. To verify a trig identity:
)
.
measure, ) , ENTER ,
24. To find the measure of an angle given the trig ratio:
.
, the trig function (sin, cos, or tan), )
, then
ENTER .
In degree mode, prepare the axes of the graph 7 by pressing ZOOM (trig). Then enter Y1=(the expression on the left side of the identity) and then Y2=(the expression on the right side of the identity). Graph these on the same screen. If the two graphs appear the same, this verifies the identity.
In degree mode, prepare the axes of the graph 7 by pressing ZOOM (trig). Then enter Y1= (the expression on the left side of the identity) and then Y2=(the expression on the right side of the identity). Graph these on the same screen. To calculate the point(s) of intersection of the graphs (which is(are) the solution(s) of the equation), use the directions under keystroke #2 found near the top of page 2.
PARAMETRIC EQUATIONS:
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What I want the calculator to do:
Which keystrokes it takes to do it:
27. To graph parametric equations:
Put the calculator in parametric mode by pressing
MODE
highlight “Par”, then
, arrow down three lines, ENTER
. Set the
window for the graph by pressing
WINDOW
and then enter the appropriate min/max/scl values for T and X. Then type
2nd
to clear the screen. Finally, go to
Quit
Y=
and enter the x and y equations in Y1 and Y2.
TROUBLESHOOTING! 28. If my data will not graph: a) Have I turned on my stat plot? b) Is my data in L1 and L2? If I do not see the data in L1, then it has been deleted. To restore L1 see the directions on page one under f. 3. c) Have I pressed ZOOM 9 or adjusted my window to fit my data? d) When all else fails, reset my memory and enter my data again.
29. (Add your own!)
30. (Add your own!)
31. (Add your own!)
To make suggestions OR to obtain a complimentary copy of the Word file for these cards, contact Ellen Hilgoe
NC EMPT Program Manager E-mail:
[email protected] NC EMPT is an outreach program of the UNC Office of the President
