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Speeding Tickets
The fine for speeding in your area is 50 plus 5 per kilometer per hour over the
limit for the first 10 kilometers, plus 10 per kilometer per hour for the next 10
kilometers, plus 20 per kilometer thereafter. Graph the piecewise function that
describes the cost of the ticket in a 45-kilometer-per-hour zone.
Problem
The fine (
Y
Y = 0
Y = 50 + 5 (X – 45)
Y = 50 + 5
Y = 50 + 5
Procedure
1. Press z. Select
and turn off all stat plots.
2. Press o. Turn off any selected functions. The
used to define piecewise functions. Enter the
the fine.
Y
=(50+5(X–45))(45<X)(X55)
1
+(100+10(X–55))(55<X)(X65)
+(200+20(X–65))(65<X)
3. Press p and set
Ignore
4. Press y ã
to
@Y
. (
are on the
produces nice values for
5. Press r to plot the functions. At what speed does the ticket exceed
250?
14-4 Applications
) as a function of kilometers per hour (
...
10 + 10 (X – 55)
...
...
10 + 10
10 + 20 (X – 65)
Func
,
Xmin = M2
and
. (They are set by
Xmax
Ymax
ä to return to the Home screen and store
QUIT
@X
and
@Y
, the distance between the centers of adjacent pixels,
VARS Window...
, and the defaults. Press y [
Dot
,
,
Xscl = 10
@X
menu.) Defining
.
TRACE
X
) is:
< X 45
0
45 < X 55
55 < X 65
65 < X
STAT PLOT
operations are
TEST
function to describe
Y=
Ymin = M5
, and
Yscl = 10
and
@Y
in step 4.)
to
@X
1
@X
and
@Y
as integers
]
.
and
5
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