Chapter 1
Page 55
173.
Temperature in Town A oscillates daily between
30
F at 4am and
60
F at 4pm. If
cos( ( ))H A B t C D
= + +
is a formula for the temperature in Town A in terms of time,
where time is measured in hours from 4 am, then A =_____, B =_____, C =_____, and
D =_____.
174.
Temperatures in a room oscillate between the low of
–10
F (at 5am) and the high of
50
F (reached at 5pm). If
cos( π)H A B t C=+
is a formula for the temperature in the
room in terms of time from 5am, then A =_____, B =_____, and C =_____.
Part A:
Part B:
1/12
Part C:
20
Learning Objectives: Find a formula for a periodic function given by graphs, tables, or
words. difficulty: medium section: 1.10
175.
Consider the function
( ) 5 cos6g t t=+
. If its period is k
π
, what is k?
Ans:
1/3
Learning Objectives: Interpret periodic functions: amplitude, period, vertical shift,
value at a point. difficulty: easy section: 1.10
176.
Consider the functions
( ) 5 sin3f x x=+
and
( ) 3sing x x=
. Which has a larger
vertical intercept?
A)
f(x)
B)
g(x)
Ans: A Learning Objectives: Interpret periodic functions: amplitude, period,
vertical shift, value at a point. difficulty: easy section: 1.10
Part A:
-15
Part B:
1/12
Part C:
0
Part D:
45
Learning Objectives: Find a formula for a periodic function given by graphs, tables, or
words. difficulty: medium section: 1.10
Chapter 1
177.
Sketch a well-labeled graph of a periodic function such that :
— f(0) = 1,050
— the period is 12
— the amplitude is 550.
Then write a few sentences illustrating how such a function might apply to a
grasshopper population.
words. difficulty: medium section: 1.10
178.
Consider the function
( ) 30 95cos(21.991 )f
=+
. Select all true statements about
this function from the list below. Answers are rounded to two decimal places.
A)
The period of the function is 0.29.
B)
The amplitude of the function is 95.
C)
The vertical shift of the function is 30.
D)
The period of the function is 0.23.
E)
The amplitude of the function is 30.
F)
The vertical shift of the function is 95.
period, vertical shift, value at a point. difficulty: easy section: 1.10
179.
Write an equation of a periodic function with amplitude 35, vertical shift 50, period
2
, and horizontal translation (phase shift) 2 units to the right.
A)
( ) 50 35cos( 2)f t t= + −
B)
( ) 35 50sin( 2)f t t= + +
C)
( ) 35cos(50 2)f t t=+
D)
( ) 50sin(2 35)f t t=−
E)
None of the above.
Chapter 1
180.
The graph of
()y f x=
is shown in the following figure. The ________ of
()fx
is
07x
, and the ________ of
()fx
is
73y−
.
181.
The graph of
()y f x=
is shown in the following figure. Estimate
(1)f
(to the
nearest integer).
Chapter 1
182.
The graph of
()y f x=
is shown in the following figure. Is the graph increasing or
decreasing at x = 3?
Ans:
increasing
value at a point. difficulty: easy section: 1 review
183.
The graph of
()y f x=
is shown in the following figure. Is the graph concave down or
concave up at x = 4?
Ans:
concave up
value at a point. difficulty: easy section: 1 review
184.
As
x→
,
3
()f x x= − →
_____.
A)
–
B)
C)
0
Chapter 1
185.
As
x→
,
4
()f x x−
=→
_____.
A)
–
B)
C)
0
graphs, or words. difficulty: medium section: 1 review
186.
As
x→
,
2 3 4
( ) 370 5 80 10f x x x x= − − + →
_____.
A)
B)
−
C)
0
graphs, or words. difficulty: medium section: 1 review
187.
As
x→ −
,
() x
f x e=→
_____.
A)
B)
0
C)
−
difficulty: medium section: 1 review
188.
The following table gives values for three different functions. Find a formula for the
linear one.
t
()ft
()gt
()ht
-1
15
21.4
1000
0
9
24.1
600
1
5
26.8
360
2
4
29.5
216
Chapter 1
189.
The following table gives values for three different functions. Find a formula for the
exponential one.
t
()ft
()gt
()ht
-1
15
21.4
1500
0
9
24.1
600
1
5
26.8
240
2
4
29.5
96
graphs, or words. difficulty: medium section: 1 review
190.
The following table gives values for three different functions. One of the functions is
neither linear nor exponential. Is that function increasing or decreasing?
t
()ft
()gt
()ht
-1
15
21.7
1200
0
9
24.1
600
1
5
26.5
300
2
4
28.9
150
Ans:
decreasing
191.
A company has cost and revenue functions given in dollars by
( ) 500 7C q q=+
and
( ) 12R q q=
. What is the effect on the break even point of doubling the fixed costs?
A)
The break even point is cut in half.
B)
The break even point is doubled.
break even points. difficulty: medium section: 1 review
192.
Write a formula for the population, P, as a function of time, t, if the population starts at
9000 and grows by 125 people each year.
doubling time, half-life. difficulty: easy section: 1 review
Chapter 1
193.
Write a formula for the population, P, as a function of time, t, if the population starts at
6000 and grows by 10% each year.
194.
Give a possible formula for the function shown in the following table.
x
0
1
2
3
4
5
()fx
–7
–4
–1
2
5
8
195.
Give a possible formula for the function shown in the following table.
x
0
1
2
3
4
5
()gx
0
–2
–8
–18
–32
–50
196.
Give a possible formula for the function shown in the following table.
x
0
1
2
3
4
5
()hx
——
4
2
1.333333
1
0.8
Chapter 1
Page 62
197.
One of the following tables of data is linear and the other one is exponential. The
formula for the linear one is
y ax b=+
. Find the values of a and b to two decimal
places.
x
0
0.50
1.00
1.50
2.00
y
3.12
2.67
2.28
1.95
1.66
x
0
0.50
1.00
1.50
2.00
y
2.71
3.94
5.17
6.40
7.63
A. a=______
B. b=_____
198.
One of the following tables of data is linear and the other one is exponential. The
formula for the exponential one is
()
x
y c d=
. Find the values of c and d to two
decimal places.
x
0
0.50
1.00
1.50
2.00
y
3.12
2.70
2.34
2.03
1.76
x
0
0.50
1.00
1.50
2.00
y
2.71
3.44
4.17
4.90
5.63
A. c=_____
B. d=_____
Part B:
0.75
Learning Objectives: Understand and interpret properties of exponential models:
doubling time, half-life. difficulty: medium section: 1 review
Part A:
2.46
Part B:
2.71
Learning Objectives: Understand and interpret properties of exponential models:
doubling time, half-life. difficulty: medium section: 1 review
Chapter 1
Page 63
199.
Write the Roman numeral of the graph that corresponds to each function.
A.
ln( ) 1
x
e+
B.
2ln x−
C.
x
e−
D.
5 4 3 2
2 2 5x x x x+ − − +
Chapter 1
200.
Of the three functions below, one is a quadratic, one is a cubic, and one is a periodic
function. Which one is h(x)?
x
0.2
0.4
0.6
0.8
1.2
()fx
-0.42
-0.65
0.96
-0.15
0.84
x
1.3
1.7
2.5
3.0
3.5
()gx
0.41
0.81
0.65
-0.10
-1.35
x
0.5
1.2
1.8
2.0
2.2
()hx
-1.13
0.13
0.03
0.00
0.05
A)
cubic
B)
periodic
C)
quadratic
difficulty: medium section: 1 review
201.
Write in factored form the equation of the polynomial graphed below. All key features
are shown.
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
11
-4 -3 -2 -1 1 2 3 4 5 6 7 8 9
x
y
graphs or words. difficulty: medium section: 1 review
Chapter 1
202.
The solid curve below is a portion of the graph of
3
( ) 8f x x=
and the dashed curve is
a portion of the graph of
0.25
() x
g x e=
. The domain of both functions is all real
numbers.Which of the following statements are true. Select all that apply.
-5
-4
-3
-2
-1
1
2
3
4
5
-3 -2 -1 1 2 3
x
y
A)
At x = 1,
( ) ( )f x g x
.
B)
For all x > 1,
( ) ( )f x g x
.
C)
As
, ( ) 0x g x→ − →
.
D)
There is only one value of x for which
( ) ( )f x g x=
.
Chapter 1
203.
Using base e and transformations, find a formula for the exponential function shown in
the graph below.
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
-3 -2 -1 1 2 3
x
y
Chapter 1
204.
Delia runs 3.1 miles from home to the park at 6 mph, jumps on her bike and returns
home in 12 minutes.
a) Sketch a well-labeled graph of Delia’s distance from home as a function of time.
b) Find the slope of each segment of the graph and interpret their meaning.
c) What does it mean to say that Delia’s velocity on the way home is inversely
proportional to the time she takes to ride home?
Learning Objectives: Determine a formula for an exponential function from data,
graphs, or words. difficulty: hard section: 1 review
205.
The elimination half-life of aspirin in plasma is estimated to be between 15 and 20
minutes. Assuming the lower estimate of 15 minutes, how long will it take a dose of 81
mg to decrease to 2/3 the original amount (54 mg) in the plasma?
A)
1.4 minutes
B)
9.7 minutes
C)
12 minutes
D)
8.8 minutes
Ans: D Learning Objectives: Understand and interpret properties of exponential
models: doubling time, half-life. difficulty: hard section: 1 review
Chapter 1
206.
Find the equation of the line passing through the points (0, –4) and (7, –3). Then
determine if the line is increasing or decreasing.