Functions Worksheet With Answer Key Page 15
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
4683
2.2 DOMAIN AND RANGE
30. A car gets the best mileage at intermediate speeds. Graph
(b) Explain how you could use the phone book to find
the gas mileage as a function of speed. Determine a rea-
the domain of f .
(c) What is the range of f ?
sonable domain and range for the function and justify
your reasoning.
Table 2.9
31. A movie theater seats 200 people. For any particular
show, the amount of money the theater makes is a func-
n
1
2
3
4
5
6
7
8
9
10
tion of the number of people, n, in attendance. If a ticket
d
1
2
1
5
9
9
0
1
1
7
costs $4.00, find the domain and range of this function.
Sketch its graph.
36. Let t be time in seconds and let r(t) be the rate, in gal-
32. (a) Table 2.8 shows the relationship between the number
lons/second, that water enters a reservoir:
of calories used per minute of walking and a person’s
6
r(t) = 800
40t.
weight in pounds.
Use the table to
(i) Determine the number of calories that a person
(a) Evaluate the expressions r(0), r(15), r(25), and
weighing 200 lb uses in a half-hour of walking.
explain their physical significance.
(b) Graph y = r(t) for 0 ≤ t ≤ 30, labeling the inter-
(ii) Describe in words the relationship between
cepts. What is the physical significance of the slope
weight and the number of calories used. Iden-
and the intercepts?
tify the dependent and independent variables
(c) For 0 ≤ t ≤ 30, when does the reservoir have the
and specify whether the function is increasing
or decreasing.
most water? When does it have the least water?
(d) What are the domain and range of r(t)?
(b) The function described in part (a)(ii) is approxi-
mately linear.
37. In month t = 0, a small group of rabbits escapes from a
(i) Estimate the equation for this function and
ship onto an island where there are no rabbits. The island
graph it.
rabbit population, p(t), in month t is given by
(ii) Give a reasonable domain and range for your
1000
p(t) =
,
t ≥ 0.
function based on the data in the table.
1 + 19(0.9)
t
(iii) Use your function to estimate how many calo-
(a) Evaluate p(0), p(10), p(50), and explain their
ries per minute a person who weighs 135 lb
meaning in terms of rabbits.
uses per minute of walking.
(b) Graph p(t) for 0 ≤ t ≤ 100. Describe the graph in
words. Does it suggest the growth in population you
would expect among rabbits on an island?
Table 2.8
Calories per minute as a function of weight
(c) Estimate the range of p(t). What does this tell you
about the rabbit population?
Weight
100 lb
120 lb
150 lb
170 lb
200 lb
220 lb
(d) Explain how you can find the range of p(t) from its
Walking
2.7
3.2
4.0
4.6
5.4
5.9
formula.
38. Bronze is an alloy or mixture of the metals copper and
tin. The properties of bronze depend on the percentage of
In Exercises 33–34, find the domain and range of the function.
copper in the mix. A chemist decides to study the proper-
ties of a given alloy of bronze as the proportion of copper
33. g(x) = a + 1/x, where a is a constant
is varied. She starts with 9 kg of bronze that contain 3
1/2
34. q(x) = (x
b)
+ 6, where b is a constant
kg of copper and 6 kg of tin and either adds or removes
copper. Let f (x) be the percentage of copper in the mix
35. The last digit, d, of a phone number is a function of n, its
if x kg of copper are added (x > 0) or removed (x < 0).
position in the phone book. Table 2.9 gives d for the first
10 listings in the 2009 New York State telephone direc-
(a) State the domain and range of f . What does your
7
tory.
The table shows that the last digit of the first listing
answer mean in the context of bronze?
is 1, the last digit of the second listing is 5, and so on. In
(b) Find a formula in terms of x for f (x).
principle we could use a phone book to figure out other
(c) If the formula you found in part (b) was not intended
values of d. For instance, if n = 300, we could count
to represent the percentage of copper in an alloy of
th
down to the 300
listing in order to determine d. So we
bronze, but instead simply defined an abstract math-
write d = f (n).
ematical function, what would be the domain and
range of this function?
(a) What is the value of f (6)?
6
Source: 1993 World Almanac. Speeds assumed are 3 mph for walking, 10 mph for bicycling, and 2 mph for swimming.
7
www6.oft.state.ny.us/telecom/phones/. Accessed February 10, 2010.
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education