11-12 Applications
The test functions of the TI
.
80 can be used to build piecewise defined functions.
Define and graph this piecewise defined function.
f(x)=
x
ñ
,
for x
≤
3
1.5x+1,
for 3
<
x
<
5
6
ì
x,
for x
≥
5
The
TEST
functions, which return 1 if true and 0 if false, can
be used to build piecewise defined functions. For example,
when x is 4 (x
≤
3) is false and will return 0.
Follow this procedure to solve the problem.
1. Press
3
and select
FUNC
.
2. Enter the first piece of the function in the
Y=
editor. This
piece is f(x)=x
ñ
for x
≤
3. It is entered as
(x
ñ
)(x
≤
3)
.
Y
ã
is
then equivalent to x
ñ
×
1 for x
≤
3 and x
ñ
×
0 for x
>
3.
3. Add the second piece of the function in the
Y=
editor. This
piece is f(x)=1.5x+1 for 3
<
x
<
5. It is entered as
(1.5x+1)(3
<
x)(x
<
5)
.
When x is less than 3, the test (3
<
x) returns 0, and the test
(x
<
5) returns 1. In this case, the second piece of the
function is equivalent to (1.5x+1)
×
0
×
1, which is 0. Only
when both of these tests are true will the second piece of
this function be anything but 0.
Graphing a Piecewise Function
Problem
Procedure
Summary of Contents for TI-80
Page 234: ...STAT PLOT FRAC TI 80 E b X T c x x x x...
Page 235: ......
