Solution Manual for Precalculus Real Mathematics, Real People, 7th Edition

NOT FOR SALE
C H A P T E R 1
Functions and Their Graphs

Section 1.1 Lines in the Plane ............................................................................ 2

Section 1.2 Functions ....................................................................................... 14

Section 1.3 Graphs of Functions ...................................................................... 20

Section 1.4 Shifting, Reflecting, and Stretching Graphs .................................. 31

Section 1.5 Combinations of Functions............................................................ 38

Section 1.6 Inverse Functions .......................................................................... 47

Section 1.7 Linear Models and Scatter Plots .................................................... 60

Chapter 1 Review ................................................................................................ 65

Chapter 1 Test ..................................................................................................... 79




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, NOT FOR SALE
C H A P T E R 1
Functions and Their Graphs
Section 1.1 Lines in the Plane
1. (a) iii (b) i (c) v (d) ii (e) iv 0 − (−10) 10 5
13. Slope = = =−
−4 − 0 −4 2
2. slope
4
3. parallel
−12 12
(−4, 0)
4. They are perpendicular to each other.

5. Since x = 3 is a vertical line, all horizontal lines are (0, −10)
perpendicular and have slope m = 0. −12


1 −4 − 4
6. Since the line y − ( −1) = ( x − 8) is in point-slope 14. Slope = = −4
4 4−2
form, the point (8, −1) lies on the line.
6


2 (2, 4)
7. (a) m = . Since the slope is positive, the line rises.
3 −6 12

Matches L2 . (4, −4)

(b) m is undefined. The line is vertical. Matches L3 . −6

(c) m = −2. The line falls. Matches L1 .
4 −1 3
(a) m = 0. The line is horizontal. Matches L2 . 15. Slope = = ; slope is undefined.
8. − 6 − ( − 6) 0
3
(b) m = − . Because the slope is negative, the line
4 6

falls. Matches L1 . (−6, 4)
(c) m = 1. Because the slope is positive, the line rises.
Matches L3 . −10 2
(−6, −1)
−2
rise 3
9. Slope = =
run 2
12 − 9 3
16. Slope = =
10. The line appears to go through (0, 8) and (2, 0). 6−4 2
8−0
Slope = = −4 13
0−2 (6, 12)
(4, 9)
11. y

m=2
m=1 −5 16
8 m = −3 −1

6
17. Since m = 0, y does not change. Three additional points
4
are (0, 1), (3, 1), and ( −1, 1).
2
(2, 3) m=0
18. Since m = 0, y does not change. Three additional points
x
2 4 6 8 10 are (0, − 2), (1, − 2), and (4, − 2).
19. Since m is undefined, x does not change and the line is
m is undefined. y
12. vertical. Three additional points are (1, 1), (1, 2), and
m=4 (1, 3).
m = −2 4
m=1
2
2 20. Because m is undefined, x does not change. Three
(−4, 1) additional points are ( −4, 0), ( −4, 3), and ( −4, 5).
x
−6 −2
21. Since m = −2, y decreases 2 for every unit increase in x.



INSTRUCTOR USE ONLY
−2 Three additional points are (1, − 11), (2, − 13), and
−4
(3, − 15).


2 © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© Cengage Learning. All Rights Reserved.

, NOT FOR SALE Section 1.1 Lines in the Plane 3


22. Since m = 4, y increases 4 for every unit increase in x. 3
28. m = , ( −2, − 5)
Three additional points are ( − 4, 8), ( − 3, 12), and 4
(− 2, 16). 3
y + 5 = ( x + 2)
1 4
23. Since m = , y increases 1 for every increase of 2 units
2 4 y + 20 = 3 x + 6
in x. Three additional points are (9, −1), (11, 0), and 0 = 3 x − 4 y − 14
(13, 1). y

1
24. Since m = − , y decreases 1 for every increase of −2 2
x
3
3 units in x. Three additional points are ( 2, − 7), (5, − 8), −2

and (8, − 9).

25. m = 3, (0, − 2) (− 2, − 5)
y + 2 = 3( x − 0)
y = 3x − 2  3x − y − 2 = 0
y
29. m is undefined, (6, − 1)
x =6
2
x − 6 = 0 vertical line
1
y
x
−2 −1 1 2 3 4
−1 6

−2 4
(0, −2)
2

x
−4 −2 2 4 (6, −1)
−2

26. m = − 3, ( − 3, 6) −4

y − 6 = −3( x + 3) −6


y − 6 = −3x − 9
30. m is undefined, ( −10, 4)
y = −3x − 3
x = 10
y
x + 10 = 0 vertical line
(−3, 6) 6
y
4

8
x (− 10, 4)
−6 −4 −2 2 4 6 4

x
−4
−12 −8 −4 4
−6 −4

1 −8
27. m = − , (2, − 3)
2
1
y − (−3) = − ( x − 2) y
2  1 3
31. m = 0,  − , 
1
y + 3 = − x +1  2 2 4

2 3  1
3

2y + 4 = −x y− = 0 x +  (− 12 , 32 ( 2
2  2
x + 2y + 4 = 0 1
3
y
y − = 0 horizontal line x
2 −3 −2 −1 1 2 3
−1
1
−2
x
−2 −1 1 2 3 4
−1


(2, − 3)
−3




INSTRUCTOR USE ONLY
−4

−5




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© Cengage Learning. All Rights Reserved.

, 4 Chapter 1
NOT FOR SALE
Functions and Their Graphs


32. m = 0, (2.3, − 8.5) 36. 3 x + 4 y = 1
y − ( −8.5) = 0( x − 2.3) 4 y = −3 x + 1
y + 8.5 = 0 horizontal line −3 1
y= x+
y 4 4
4 3
2 Slope: −
x 4
−8 −6 −4 −2 2 4 6 8 10
−4  1
−6
y-intercept:  0, 
(2.3, −8.5)  4
− 10
− 12  1
− 14
The line passes through  0,  and falls 3 units for each
− 16
 4
horizontal increase of 4 units.
33. Begin by letting x = 7 correspond to 2007. Then using
37. 2 x − 5 y + 10 = 0
the points (7, 1.5) and (13, 1.7), you have
−5 y = −2 x − 10
1.7 − 1.5 0.2 1 2
m = = = y= x+2
13 − 7 6 30 5
1
y − 1.5 = ( x − 7) Slope:
2
30 5
1 7
y − 1.5 = x − y-intercept: (0, 2)
30 30
The line passes through (0, 2) and rises 2 units for each
1 19
y = x + horizontal increase of 5 units.
30 15
1 19 38. 4 x − 3 y − 9 = 0
When x = 19: y = (19) + = $1.9 million
30 15 −3 y = − 4 x + 9
4
34. Begin by letting x = 4 correspond to 2004. Then using y = x −3
3
the points ( 4, 348,000) and (13, 555,000), you have
4
555,000 − 348,000 207,000 Slope:
m = = = 23,000 3
13 − 4 9
y-intercept: (0, − 3)
y − 348,000 = 23,000( x − 4) The line passes through (0, − 3) and rises 4 units for
y − 348,000 = 23,000 x − 92,000 each horizontal increase of 3 units.
y = 23,000 x + 256,000
39. x = −6
When x = 19: Slope is undefined; no y-intercept.
y = 23,000(19) + 256,000 = $693,000 The line is vertical and passes through ( − 6, 0).
35. 2 x − 3 y = 9 40. y = 12
−3y = − 2x + 9 Slope: 0
2 y-intercept: (0, 12)
y = x −3
3 The line is horizontal and passes through (0, 12).
2
Slope: 41. 3 y + 2 = 0
3
3 y = −2
y-intercept: (0, − 3)
2
y=−
The line passes through (0, − 3) and rises 2 units for each 3
horizontal increase of 3 units. Slope: 0
 2
y-intercept:  0, − 
 3

 2
The line is horizontal and passes through  0, −  .


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 3



© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© Cengage Learning. All Rights Reserved.