Functions Worksheet With Answer Key Page 44
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46112
Chapter Two FUNCTIONS
62. Table 2.31 shows the cost, C(m), in dollars, of a taxi ride
69. (a) The Fibonacci sequence is a sequence of numbers
as a function of the number of miles, m, traveled.
that begins 1, 1, 2, 3, 5, . . .. Each term in the se-
quence is the sum of the two preceding terms. For
(a) Estimate and interpret C(3.5) in practical terms.
example,
1
(b) Assume C is invertible. What does C
(3.5) mean
1
in practical terms? Estimate C
(3.5).
2 = 1 + 1,
3 = 2 + 1,
5 = 2 + 3, . . . .
Table 2.31
Based on this observation, complete the following
th
table of values for f (n), the n
term in the Fi-
m
0
1
2
3
4
5
bonacci sequence.
C(m)
0
2.50
4.00
5.50
7.00
8.50
n
1
2
3
4
5
6
7
8
9
10
11
12
63. The perimeter, in meters, of a square whose side is s me-
ters is given by P = 4s.
f (n)
1
1
2
3
5
(a) Write this formula using function notation, where f
is the name of the function.
(b) The table of values in part (a) can be completed even
(b) Evaluate f (s + 4) and interpret its meaning.
though we don’t have a formula for f (n). Does the
(c) Evaluate f (s) + 4 and interpret its meaning.
fact that we don’t have a formula mean that f (n) is
1
(d) What are the units of f
(6)?
not a function?
(c) Are you able to evaluate the following expressions
64. (a) Find the side, s = f (d), of a square as a function of
using parts (a) and (b)? If so, do so; if not, explain
its diagonal d.
why not.
(b) Find the area, A = g(s), of a square as a function of
its side s.
f (0),
f ( 1),
f ( 2),
f (0.5).
(c) Find the area A = h(d) as a function of d.
(d) What is the relation between f , g, and h?
70. Table 2.32 contains values of g(t). Each function in
65. Suppose that f (x) is invertible and that both f and
parts (a)–(e) is a translation of g(t). Find a possible for-
1
f
are defined for all values of x. Let f (2) = 3 and
mula for each of these functions in terms of g.
1
f
(5) = 4. Evaluate the following expressions, or,
if the given information is insufficient, write unknown.
Table 2.32
1
1
(a) f
(3)
(b) f
(4)
(c) f (4)
t
1
0.5
0
0.5
1
2
66. Let k(x) = 6
x
.
g(t)
0.5
0.8
1.0
0.9
0.6
(a) Find a point on the graph of k(x) whose x-
coordinate is 2.
(b) Find two points on the graph whose y-coordinates
(a)
are 2.
t
1
0.5
0
0.5
1
(c) Graph k(x) and locate the points in parts (a) and (b).
a(t)
1.0
1.3
1.50
1.4
1.1
(d) Let p = 2. Calculate k(p)
k(p
1).
√
67. (a) Find a point on the graph of h(x) =
x + 4 whose
(b)
t
1
0.5
0
0.5
1
x-coordinate is 5.
b(t)
1.0
0.9
0.6
0.1
0.4
(b) Find a point on the graph whose y-coordinate is 5.
(c) Graph h(x) and mark the points in parts (a) and (b).
(d) Let p = 2. Calculate h(p + 1)
h(p).
(c)
t
1
0.5
0
0.5
1
68. Let t(x) be the time required, in seconds, to melt 1 gram
c(t)
0.7
0.6
0.3
0.2
0.7
of a compound at x
◦
C.
(a) Express the following statement as an equation us-
(d)
ing t(x): It takes 272 seconds to melt 1 gram of the
t
1
0.5
0
.5
1
compound at 400
◦
C.
d(t)
0
0.5
0.8
1.0
0.9
(b) Explain the following equations in words:
1
(i) t(800) = 136
(ii) t
(68) = 1600
(e)
t
1
0.5
0
0.5
1
(c) Above a certain temperature, doubling the temper-
ature, x, halves the melting time. Express this fact
e(t)
1.2
1.7
2.0
2.2
2.1
with an equation involving t(x).
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