Question

A roller coaster accelerates from a stop. Table 1 is represented by a quadratic function
f
(
t
)
, where
f
(
t
)
is the distance the roller coaster has traveled, in feet, based on the time,
t
, in seconds, since it started moving.

At the end of the ride, the same roller coaster begins to slow down as it approaches the station. Table 2 is represented by a quadratic function
g
(
s
)
, where
g
(
s
)
is the safe stopping distance, in feet, based on the speed,
s
, in miles per hour the roller coaster is traveling.

image
The table for
g
(
s
)
is modeled by the function
g
(
s
)
=
0.15
s
2
.





What is the range of this function given the domain
0
≤
s
≤
60
?



A.
g
(
s
)
≥
0

B.
g
(
s
)
≤
540

C.
0
≤
g
(
s
)
≤
540

D.
15
≤
g
(
s
)
≤
540

Answer 1

g(s) = 0.15 s^2 is increasing for s ≥ 0, with g(0)=0 and g(60)=0.15(3600)=540. Thus 0 ≤ g(s) ≤ 540, so answer C.