Texas Instruments TI-89 Manual page 15

TI-89 Guide
1.1.10 SUMMARY OF ESTI MATI NG AND SOLVI NG METHODS Use the method you prefer.
When you are asked to estimate or approximate an output or an input value, you can:
•
Trace a graph
•
Use close values obtained from the TI-89 table
When you are asked to find or determine an output or an input value, you should:
•
Evaluate an output on the graphics screen
•
Evaluate an output on the home screen
•
Evaluate an output value using the table
•
Find an input using the solve instruction or the numeric solver
•
Find an input value from the graphic screen (using the x-intercept
method or the intersection method)
1.3 Constructed Functions
Your calculator can find output values of and graph combinations of functions in the same way
that you do these things for a single function. The only additional information you need is how
to enter constructed functions in the graphing list or on the home screen.
1.3.1 FI NDI NG THE SUM, DI FFERENCE, PRODUCT, QUOTI ENT OR COMPOSI TE
FUNCTI ON
and that a function g has been entered in
evaluate, graph, and actually find the symbolic form of these constructed functions:
Enter
+
y 1 ( x ) y 2 ( x )
Enter
–
y 1 ( x ) y 2 ( x )
Enter
*
y 1 ( x ) y 2 ( x )
Enter
/
y 1 ( x ) y 2 ( x )
Enter to obtain the composite function (f
( )
y 1 y 2 ( x )
1.3.2 FI NDI NG A DI FFERENCE FUNCTI ON
that are given on page 31 of Section 1.3 of Calculus Concepts: Sales = S(t) = 3.570(1.105
million dollars and costs = C(t) =
We use the functions on the home screen, but you can also use the
you are in the
Y=
NOTE: Before you start a problem in which you want a symbolic result (i.e., a formula rather
than a number), clear all individual letter variable names with
or
ENTER 2nd F1 [F6] 1 [Clear a-z] ENTER
On the home screen, define S with
3 (S) ( ) = 3 . 570 ( 1 . 105 ^
T
define C with
. 2 ^ 2 +
T
•
As we previously mentioned, you can use any input variable on the home screen. We
choose to use t because it is given as the input variable in the text illustration. However, if
you prefer x, replace every t by x in the instructions.
Copyright © Houghton Mifflin Company. All rights reserved.
Suppose that a function f has been entered in
to obtain the sum function (f + g)(x) = f(x) + g(x).
to obtain the difference function (f – g)(x) = f(x) – g(x).
to obtain the product function (f
to obtain the quotient function (f ÷ g)(x) =
−
39.2t
list, the symbolic form of the constructed function is not displayed.
F4 [Other] 1 [Define] alpha
F4 1 [Define] alpha ) (C) (
. +
5 4 0 1 T 1 0 6 1
y 1
in the list or defined as
Y=
y 2
⋅ ⋅
g)(x) = f(x)
f x ( )
g x ( )
g)(x) = f(g(x)).
o
We illustrate this technique with the functions
2
+ 540.1t + 1061.0 thousand dollars t years after 1996.
2nd F1 [F6] 2 [NewProb]
. (See the warning message on the next page.)
and
) ENTER
T
( − )
) =
T
ENTER .
TI 89-15
(Section 1.1.4)
(Sections 1.1.3, 1.1.5, 1.1.7)
(Section 1.1.3)
(Section 1.1.5)
(Section 1.1.6)
(Sections 1.1.7, 1.1.8)
(Section 1.1.9)
in the list or defined as
Y=
. Your TI-89 will
y 2 ( x )
g(x).
.
list locations. However, if
Y=
39
y 1 ( x )
t
)