Download Workshop 3 - Arapahoe Community College

1
Arapahoe Community College
MAT 111 - Graphing Calculator Techniques for Survey of Algebra
TI-83 Graphing Calculator
Workshop #3
Functions
This workshop will
1)
2)
3)
4)
investigate functions accessed through the keyboard and
functions accessed through menus,
offer practice in using the table of functions and
instructions in the user’s manual,
demonstrate a method for evaluating functions,
investigate the table feature of the TI-83.
Functions Accessed Through the Keyboard
Exponent Key
The exponent key is used to calculate a base raised to an exponent. The base is
entered first then the <4, 5>, then the exponent.
<4, 5>
. Calculated value __________.
1)
Find 27. Press
8
2)
Find 5 . Calculated value ______________.
You may need to use parentheses in the following:
3)
Find –28. Answer –256.
4)
Find (-2) 8. Answer 256.
5)
Find 641/2. Answer 8.
Square Key and Square Root Key
To square a number, enter the number first then press the square key <5, 1>. To
take the square root of a number press the square root key 2nd, <5, 1> and then
the number.
1) Find π 2. Calculated value ________________.
2) Find π . Calculated value ________________.
3) Find − π . Calculated value _______________.
2
Reciprocal Key
To take the reciprocal of a number, enter the number and then press the x-1 key,
<4, 1>.
1)
2)
3)
4)
Press
<4, 1>. FRAC.
Calculated value __________________.
Find the reciprocal of –27. Calculated value ________________.
Find the reciprocal of 5/33. Calculated value ________________.
Find the reciprocal of π . Calculated value ______________.
Functions Accessed Through Menus
There are numerous functions available through menus or the catalog. In
fact, the catalog gives you a good idea of all the functions available. There
are two types of functions: single argument functions and functions which
have more than one argument.
You can employ single argument functions by accessing the function
name using a menu or the catalog and then by entering the argument of
the function. An example of a single argument function is the absolute
value function. To find − 63 , enter abs (from the catalog) and then
, and press
.
Table of Functions and Instructions
The alphabetical listing of operations beginning on page A-2 of the user'
s
manual is a very useful listing for performing operations on the TI-83. This
table contains all of the operations available on the TI-83.
1)
2)
3)
4)
5)
Look up abs in the listing of operations.
The first column gives the operation and the necessary
arguments. The abs operation has one argument.
The second column lets you know the possibilities for these
arguments. For abs, you could use a real number,
expression, list or matrix. Or, looking at the second row, the
argument could be a complex number or list. The result is
the absolute value of the real argument or the magnitude of
the complex argument.
The third column gives you the keystrokes to access the
operation as well as page numbers to seek for further
information for a particular application.
.
Find − 63 by entering abs
Calculated value _______
3
6)
Find 34 by entering abs
Calculated value ______
.
Look up these operations in your manual and give a brief description of each.
gcd
arguments __________________________________________________
result ______________________________________________________
keystrokes __________________________________________________
sci
arguments __________________________________________________
result ______________________________________________________
keystrokes __________________________________________________
fMax
arguments __________________________________________________
result ______________________________________________________
keystrokes __________________________________________________
seq
arguments __________________________________________________
result ______________________________________________________
keystrokes __________________________________________________
You will now practice with two of the above operations.
First, you can find the x coordinate of the maximum value of the function defined
by -x2 +3x -5 between -10 and 10. The vertex (turning point) of this function is at
(1.5, -2.75).
1)
Press
. Your screen should match the screen below. Press
calculate.
2)
Report the calculated value.______________
to
4
3)
4)
To find the maximum function value, press
retype in the expression -x2 +3x - 5 and press
Calculated Value____________________.
. Then
.
Table Feature
You can evaluate functions at many different values of the independent
variable using a table. To use a table, you must enter functions in the
equation editor of the Y= menu and define the values of the independent
variable through the TBLSET (
) option. The function values
are displayed in columns of the table. The columns are in the order in
which the functions are entered in the equation editor of the Y= menu.
1)
2)
3)
4)
Press This is the left-most blue key just under the screen.
Press
on any lines that have "leftover" expressions.
.
By Y1= enter
By Y2= enter
.
5)
Press
6)
You can use the arrow keys to move around the table.
Use the down arrow key until you reach x = 11 to find 112 and 113.
112 = ____________ and 113 = __________.
7)
Go to TBLSET using
to access the TABLE.
and the second blue key
.
5
8)
9)
Change TblStart to -4 by pressing
Change Tbl to 2 by pressing
10)
Press
11)
What x value is at the start of the table? ________
.
and then
.
to look at the Table again.
12)
What is the increment or change in x as you go down the table?
____
You can also enter unevenly spaced values for the independent variable by using
the ASK option under the TBLSET menu.
X
-7
1.8
13)
14)
Select the TBLSET menu.
Highlight the ASK option next to Indpnt and press
15)
16)
Select the TABLE menu.
In the first column, enter -7, 1.8, -2.3, 15, 242, -101.2 for x by typing
. Be sure to use the gray ( - )
in each number, followed by
minus key for negative numbers.
17)
Fill in the following table.
X2
X3
.
6
-2.3
15
242
-101.2