Texas Instruments TI-85 User Manual
Page 17
Chapter 1
B-17
Copyright © Houghton Mifflin Company. All rights reserved.
On the TI-85
,
¥
The TI-85 interprets
y
1
(
y
2
) as the product of
y
1
and
y
2
. To have the calculator graph t h e
composite function f(g(x)), you should substitute g(x) everywhere an x appears in f(x).
For instance, if f(x) = x
2
- 1 is in
y
1
and g(x) = 0.3x + 5 is in
y
2
, enter
y
7
=
y
22
Ð 1 for t h e
composite function (f
o
g)(x) .
On the TI-86
,
¥ Enter
y
1
(
y
2
) in
y
7
to obtain the composite function (f
o
g)(x) = f(g(x)).
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
Piecewise continuous
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
P t
t
t
t
t
( )
.
.
.
.
=
+
£ <
+
£ £
м
н
о
-
23 514
3903 667
85
90
9 1
972 6
90
93
thousand people when
thousand people when
where t is the number of years since 1900.
Enter the function P(t), using x as the input variable,
in the
y
1
location of the
y(x)=
list using the keystrokes
(
(–)
23.514 x-
VAR
+
3903.667 )
(
x-
VAR
2nd
2
(
TEST
)
F2
(
<
)
90
)
+
(
9.1 x-
VAR
+
972.6 )
(
x-
VAR
F5
(
³)
90
)
.
Each piece of the function and
its corresponding input must
be enclosed in parentheses.
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
F1
ZOOM
(
ZFIT
) to graph P(x).
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
F5
(
GRAPH
) .