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On the TI-85,
¥
The TI-85 interprets y
composite function f(g(x)), you should substitute g(x) everywhere an x appears in f(x).
For instance, if f(x) = x
composite function (f
On the TI-86,
¥ Enter y
(y
) in y
1
2
Both Your calculator will evaluate and graph these constructed functions. Although it will
not give you an algebraic formula for a constructed function, you can check your algebra by
evaluating the calculator-constructed function and your constructed function at several
different points. (You will very likely have to reset the horizontal and vertical views when
graphing constructed functions.)
1.3.1 GRAPHING PIECEWISE CONTINUOUS FUNCTIONS
functions are used throughout the text. It is often helpful to use your calculator to graph and
evaluate outputs of piecewise continuous functions. Consider the following example.
The population of West Virginia from 1985 through 1993 can be modeled by
ì
=
í
P t
( )
î
where t is the number of years since 1900.
Enter the function P(t), using x as the input variable,
in the y
location of the y(x)= list using the keystrokes
1
(
23.514 x-
(–)
x-
VAR
2nd
2
+
9.1 x-
VAR
90
) .
Notice that the function is defined only when the input
is between 85 and 93. You could find P(85) and P(93) to
help you set the vertical view. However, we choose to
let the calculator set the vertical view.
Set the horizontal view xMin = 85 and xMax = 93. Press
GRAPH
F3
MORE
If you wish to see the ÒbreakÓ in the function where
the two pieces join, the width of the screen must be a
multiple of 12.6 and include 90.
Since 90 Ð 0.5(12.6) = 83.7 and 90 + 0.5(12.6) = 96.3,
change xMin and xMax to these values. Press
Copyright © Houghton Mifflin Company. All rights reserved.
(y
) as the product of y
1
2
2
- 1 is in y
and g(x) = 0.3x + 5 is in y
1
g)(x) .
o
to obtain the composite function (f
7
-
+
23 514
.
t
3903 667
.
thousand people when
+
9 1
.
t
972 6
.
thousand people when
+
3903.667
VAR
(
)
(<) 90
TEST
F2
972.6
)
(
x-
VAR
(
F1
ZOOM
ZFIT
and y
. To have the calculator graph t h e
1
2
g)(x) = f(g(x)).
o
85
£ £
90
t
93
)
(
+
)
(
(³)
F5
) to graph P(x).
(
) .
F5
GRAPH
Chapter 1
2 2
, enter y
= y
Ð 1 for t h e
2
7
Piecewise continuous
£ <
t
90
Each piece of the function and
its corresponding input must
be enclosed in parentheses.
B-17
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