Checkpoint
1.1
and
1.2
Domain = range =
1.3
1.4
The domain is
1.5
1.6
1.7
is odd.
1.8
Domain = range =
1.9
The point-slope form is
The slope-intercept form is
1.10
The zeros are The parabola opens upward.
1.11
The domain is the set of real numbers such that The range is the set
1.12
The domain of is The domain of is
1.13
Algebraic
1.14
1.15
1.16
Shift the graph to the left 1 unit, reflect about the -axis, then shift down 4 units.
1.17
330°
1.18
1.19
ft
1.20
for
1.22
To graph the graph of needs to be compressed horizontally by a factor of 4, then stretched vertically by a factor of 3, then shifted down 5 units. The function will have a period of and an amplitude of 3.
1.23
No.
1.24
The domain of is The range of is
1.25
1.26
The domain of is The range of is The inverse function is given by the formula
1.27
1.28
1.29
After years, there will be approximately
1.30
1.31
1.32
1.33
The magnitude earthquake is roughly times as severe as the magnitude earthquake.
1.34
1.35
Section 1.1 Exercises
1.
a. Domain = range = b. Yes, a function
3.
a. Domain = range = b. No, not a function
5.
a. Domain = range = b. Yes, a function
7.
a. b. 3 c. 13 d. e. f.
9.
a. Undefined b. 2 c. d. e f.
11.
a. b. c. d. e. f.
13.
a. 9 b. 9 c. 9 d. 9 e. 9 f. 9
15.
no y-intercept
17.
19.
no x-intercept;
21.
no intercepts
23.
25.
27.
29.
Function; a. Domain: all real numbers, range: b. c. d. and e. and f. Not constant g. y-axis h. Even
31.
Function; a. Domain: all real numbers, range: b. c. d. e. None f. Not constant g. Origin h. Odd
33.
Function; a. Domain: range: b. c. d. e. Not decreasing f. and g. Origin h. Odd
35.
Function; a. Domain: range: b. c. d. Not increasing e. f. g. No Symmetry h. Neither
37.
a. all real numbers b. all real numbers c. all real numbers d.
39.
a. all real numbers b. all real numbers c. all real numbers d.
41.
a. b. 6; c. d.
43.
a. all real numbers b. all real numbers
45.
a. all real numbers b. all real numbers
47.
a. b.
49.
a. Yes, because there is only one winner for each year. b. No, because there are three teams that won more than once during the years 2001 to 2012.
51.
a. b. a cube of side length 11.8 each has a volume of approximately 1643 cubic units.
53.
a. b. i. therefore, the vehicle can travel 300 mi on a full tank of gas. Ii. therefore, the vehicle can travel 225 mi on 3/4 of a tank of gas. c. Domain: range: d. The driver had to stop at least once, given that it takes approximately 39 gal of gas to drive a total of 578 mi.
55.
a. b. Exact: approximately 95 cm2 c. d. Exact: approximately 35 cm
57.
a. b. $962.50, $1090, $1217.50 c. 77 skateboards
Section 1.2 Exercises
59.
a. −1 b. Decreasing
61.
a. 3/4 b. Increasing
63.
a. 4/3 b. Increasing
65.
a. 0 b. Horizontal
67.
69.
71.
73.
75.
a. b.
77.
a. b.
79.
a. b.
81.
a. b.
83.
a. 2 b. c. −5 d. Both ends rise e. Neither
85.
a. 2 b. c. −1 d. Both ends rise e. Even
87.
a. 3 b. 0, c. 0 d. Left end rises, right end falls e. Odd
89.
91.
93.
95.
a. b.
97.
a. b.
99.
True;
101.
False; where is a real-valued constant, is a power function
103.
a. b. means that the initial purchase price of the equipment is $20,500; means that in 7.5 years the computer equipment has no value. c. $6835 d. In approximately 6.4 years
105.
a. b. $245 c. 167 cupcakes
107.
a. b. In 4 years, the value of the car is $20,000.
109.
$30,337.50
111.
96% of the total capacity
Section 1.3 Exercises
113.
115.
117.
119.
121.
123.
125.
127.
129.
a. b.
131.
a. b.
133.
a. b.
135.
a. b.
137.
a. b.
139.
141.
143.
145.
155.
157.
159.
161.
163.
165.
167.
a. 1 b. c. units to the right
169.
a. b. c. No phase shift
171.
a. 3 b. c. units to the left
173.
Approximately 42 in.
175.
a. 0.550 rad/sec b. 0.236 rad/sec c. 0.698 rad/min d. 1.697 rad/min
177.
179.
a. π/184; the voltage repeats every π/184 sec b. Approximately 59 periods
181.
a. Amplitude = b. c. 14 hours later, or 2 p.m. d.
Section 1.4 Exercises
183.
Not one-to-one
185.
Not one-to-one
187.
One-to-one
189.
a. b. Domain
191.
a. b. Domain: all real numbers, range: all real numbers
193.
a. b. Domain: range:
195.
197.
199.
These are inverses.
201.
These are not inverses.
203.
These are inverses.
205.
These are inverses.
207.
209.
211.
213.
215.
217.
a. b. The inverse function determines the distance from the center of the artery at which blood is flowing with velocity V. c. 0.1 cm; 0.14 cm; 0.17 cm
219.
a. $31,250, $66,667, $107,143 b. c. 34 ppb
221.
a. b. c.
223.
so, the temperature occurs on June 21 and August 15
225.
227.
the expression does not equal 2.1 since —in other words, it is not in the restricted domain of since 2.1 is in the restricted domain of
Section 1.5 Exercises
229.
a. 125 b. 2.24 c. 9.74
231.
a. 0.01 b. 10,000 c. 46.42
233.
d
235.
b
237.
e
239.
Domain: all real numbers, range:
241.
Domain: all real numbers, range:
243.
Domain: all real numbers, range:
245.
Domain: all real numbers, range:
247.
249.
251.
253.
255.
257.
259.
261.
263.
265.
Domain: range:
267.
Domain: range:
269.
Domain: range:
271.
273.
275.
277.
279.
281.
283.
285.
287.
289.
291.
293.
295.
297.
299.
301.
Approximately $131,653 is accumulated in 5 years.
303.
i. a. pH = 8 b. Base ii. a. pH = 3 b. Acid iii. a. pH = 4 b. Acid
305.
a. million b. 94 years from 2013, or in 2107
307.
a. b. hours
309.
The San Francisco earthquake was times more intense than the Japanese earthquake.
Review Exercises
311.
False
313.
False
315.
Domain: range: all real numbers
317.
Domain: and range: all real numbers
319.
Degree of 3, -intercept: 0, zeros: 0,
321.
323.
325.
4
327.
One-to-one; yes, the function has an inverse; inverse:
329.
331.
a. b. 100 shirts
333.
The population is less than 20,000 from December 8 through January 23 and more than 140,000 from May 29 through August 2
335.
78.51%