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CHAPTER 1
Functions, Graphs, and Limits
Section 1.1 The Cartesian Plane and the Distance Formula..................................14
Section 1.2 Graphs of Equations.............................................................................18
Section 1.3 Lines in the Plane and Slope................................................................24
Mid-Chapter Quiz Solutions......................................................................................30
Section 1.4 Functions...............................................................................................33
Section 1.5 Limits....................................................................................................38
Section 1.6 Continuity.............................................................................................42
Review Exercises..........................................................................................................45
Chapter Test Solutions................................................................................................51
Practice Test ...............................................................................................................54
Copyright © Houghton Mifflin Company. All rights reserved.
CHAPTER 1
Functions, Graphs, and Limits
Section 1.1 The Cartesian Plane and the Distance Formula
Skills Review
2 22
22
2 8. 62−+−2−y =52
1. 36−+⎡1−−5⎤=−3+6 ()()
() ()()
⎣⎦
2 2
22
=+936 ⎛⎞
62 2y 52
−+−− =
()()
⎜⎟
()
= 45 ⎝⎠
22
62−+−2−y =52
= 35 ()()
2 2
42+−−y =52
()
2
222 2
−−20+⎡−7−−3⎤= −2+−4
2.
() ()()() 16 2 52
⎣⎦ +−−y =
()
=+416 2
−−23y =6
()
= 20 −−26y =±
= 25 −=y ±62+
62
54 y =−∓
+−
3. ( ) = 1 y =−8, 4
22
x +−5
−+31− ( )
( ) −4 9. = 7
4. ==−2 2
22
x +−51=4
()
5. 27 +=12 3 3 +2 3 =5 3 x = 19
6. 81−=822−32=−2 −+7 y
10. 2 = −3
22
37x 445
7. −+−=
()() −76+=y −
2 2 y = 1
22
⎛⎞
37445
−+x −=
()()
⎜⎟
()
⎝⎠
22
37−+x −4=45
()()
2 2
33−+x =45
()
2
39−+x =45
()
2
33−=x 6
()
36−=x ±
36
−=x −±
x = 36∓
x =−3, 9
1. y
(−5, 3) 3
2
1 (2, 0)
x
−52−4 −3 −2 −1 3
−2 (1, −1)
(−2, −4)−3
−4
−5 (1, −6)
−6
14 Copyright © Houghton Mifflin Company. All rights reserved.
Section 1.1 The Cartesian Plane and the Distance Formula 15
3. (a) y 9. (a) y
5 (5, 5) (1, 3)
2
4
3 (4, 3) (−1, 1) 0, 1 + 3
2
2 x
−21−1 2
1 (3, 1) −1
x
1 2 3 4 5
2 2
(b) d =−11−+1−3
()
22 ()
(b) d =−53+5−1=4+16=25
()()
35++15 =+41−23+3
⎛⎞
(c) Midpoint ==,4,3
()
⎜⎟
22 =−823
⎝⎠
y ⎛⎞⎛⎞
11+−
5. (a) () 31++31
(c) Midpoint
==,0,
2 ⎜⎟⎜⎟
⎜⎟⎜⎟
1 22 2
, 1 ⎝⎠⎝⎠
()
2
x y
−4 −2 2 4 11. (a)
1 6 (0.5, 6)
− , −2
( )
2
4
−4 2
3 (0.25, 0.6)
− , −5
( ) x
2
−6 −64−4 −2 2 6
−2
−4 (0, −4.8)
2 2 −6
(b) d =⎡32−12⎤+5−1
()() ( )
⎣⎦
=+436 2 2
(b) d =−0.5 0 +6−−4.8
()()
= 210 ()
⎛+12 −32 1+−5⎞ =+0.25 116.64
(c) Midpoint = ( ) ( ), ( )
⎜⎟=116.89
22
⎝⎠
00+−.54.8+6
1 ⎛⎞
⎛⎞ (c) Midpoint ==,0.25,0.6
=−,2− ()
⎜⎟ ⎜⎟
22
2 ⎝⎠
⎝⎠
7. (a) y 13. (a) a = 4
14 (4, 14) 3b =
10 22
c =−40+3−0
(3, 8) ()()
6 =+16 9
2 (2, 2) = 5
x 22 2
2 4 6 8 (b) ab+=16 +9 =25 =c
22 15. (a) a=10
(b) d =−42+14−2
()()
=+4 144 3b =
22
c =+73+4−1
= 237 ()()
24++214 =+100 9
⎛⎞
(c) Midpoint ==,3,8
()
⎜⎟
22
⎝⎠ =109
22 2
(b) ab+=100 +9 =109 =c
Copyright © Houghton Mifflin Company. All rights reserved.
16 Chapter 1 Functions, Graphs, and Limits
22 22
d =−+−
17. 30 71 21. d = x −+14−−0=5
1 ()() ()()
=+ 2
936 xx−+217=5
= 45 2
xx−+=21725
2
= 35 xx−−28=0
22 xx−+42=0
d =−40+−1−1 ()()
2 ()()
=+16 4 x =−4, 2
= 20 22
−+y−=
23. d = 30 0 8
()()
= 25 2
98+=y
2 2 2
d =−34+⎡7−−1⎤ 96+=y 4
3 () ()
⎣⎦
164 y2 = 55
=+
= 65 y =± 55
222
Because dd+=d,the figure is a right triangle. 222
123 25. (a) dd=+16 5 , >0
y d2 = 281
(3, 7)
6 d =≈281 16.76 feet
d1 (b) A = 2 40 281
()
4 ( )
d3
2 = 80 281
(0, 1) ≈ 1341.04square feet
x
2 d 6
2 (4, −1) 70
27.
22
19. d =−10+2−0
1 ()()
=+14
= 5 5 16
60
22 Answers will vary. Let x = 6 correspond to 1996. The
d =−+−
31 32
2 ()()
=+ number of subscribers steadily increased from 1996 to
41 2001 and then steadily decreased from 2001 to 2005.
= 5 29. From the graph you can estimate the values to be:
22
=−+−
d 23 13
3 ()() (a) March 2005: 10,700
=+ (b) December 2005: 10,900
14
= 5 (c) May 2006: 11,400
22 (d) January 2007: 12,500
d =−02+0−1
4 ()()
=+41 31. (a) 1990: $92,000
= 5 (b) 1992: $100,000
(c) 1997: $122,000
Because dd==d=d,the figure is a
1234 (d) 2005: $208,000
parallelogram.
y
3 (3, 3)
d2
(1, 2)
2 d3
d1
1 (2, 1)
d4
(0, 0) x
1 2 3
Copyright © Houghton Mifflin Company. All rights reserved.
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