Functions Worksheet With Answer Key Page 40
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46108
Chapter Two FUNCTIONS
24. The rate at which water is entering a reservoir is given for
26. Match each story with the table and graph which best
time t > 0 by the graph in Figure 2.43. A negative rate
represent it.
means that water is leaving the reservoir. In parts (a)–(d),
(a) When you study a foreign language, the number of
give the largest interval on which:
new verbs you learn increases rapidly at first, but
(a) The volume of water is increasing.
slows almost to a halt as you approach your satu-
(b) The volume of water is constant.
ration level.
(c) The volume of water is increasing fastest.
(b) You board an airplane in Philadelphia heading west.
(d) The volume of water is decreasing.
Your distance from the Atlantic Ocean, in kilome-
ters, increases at a constant rate.
rate
(c) The interest on your savings plan is compounded an-
nually. At first your balance grows slowly, but its rate
of growth continues to increase.
t
time,
E F
H I
x
O
A
B
C D
G
0
5
10
15
20
25
(E)
y
20
275
360
390
395
399
x
0
5
10
15
20
25
Figure 2.43
(F)
y
20
36
66
120
220
400
25. Match each of the following descriptions with an appro-
x
0
5
10
15
20
25
priate graph and table of values.
(G)
y
20
95
170
245
320
395
(a) The weight of your jumbo box of Fruity Flakes de-
creases by an equal amount every week.
(b) The machinery depreciated rapidly at first, but its
(I)
(II)
(III)
value declined more slowly as time went on.
(c) In free fall, your distance from the ground decreases
faster and faster.
(d) For a while it looked as if the decline in profits was
slowing down, but then they began declining ever
more rapidly.
27. The relationship between the swimming speed U (in
cm/sec) of a salmon to the length l of the salmon (in cm)
x
0
1
2
3
4
5
(E)
17
is given by the function
y
400
384
336
256
144
0
√
U = 19.5
l.
x
0
1
2
3
4
5
(F)
y
400
320
240
160
80
0
(a) If one salmon is 4 times the length of another
salmon, how are their swimming speeds related?
√
x
0
1
2
3
4
5
(G)
(b) Graph the function U = 19.5
l. Describe the graph
y
400
184
98
63
49
43
using words such as increasing, decreasing, concave
up, concave down.
x
0
1
2
3
4
5
(H)
(c) Using a property that you described in part (b), an-
y
412
265
226
224
185
38
swer the question “Do larger salmon swim faster
than smaller ones?”
(d) Using a property that you described in part (b), an-
(I)
(II)
swer the question “Imagine four salmon—two small
and two large. The smaller salmon differ in length by
1 cm, as do the two larger. Is the difference in speed
between the two smaller fish, greater than, equal to,
or smaller than the difference in speed between the
two larger fish?”
(III)
(IV)
28. The graph of f is concave down for 0 ≤ x ≤ 6. Which
f (3)
f (1)
f (5)
f (3)
is bigger:
or
? Why?
3
1
5
3
17
From K. Schmidt-Nielsen, Scaling, Why is Animal Size so Important? (Cambridge: CUP, 1984).
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