REVIEW FOR
1ST SEM.
2016-17
FINAL
ANSWERS
CH 1…..PG. 117
99. circle, center ( -1,3) radius 1
101. no graph
111. no symm
@ 200. symm. with y axis
@201. Neither
@ 202. Symm. with x axis
@203. Origin symm.
@204. Neither
117. y axis
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CH 2……PG. 204
7. ( - inf, inf )
9. [ - 4, inf ]
11. all x, x not = to -2, -1, 0
41. a) shift 8 up b) 8 left
d) 2 rt,
down 2
e) reflect across y axis
f) reflect across both x, y axis
g) reflect across x axis
43. a) neither b) odd c) even
d) neither
45. y = (x+2)^2 – 3
47. g( - 1 ) = - 7
51. a) x^2 - 6x + 6
e) 9x^2 - 15x + 6
f) -3x^2 + 9x - 2
63. [ 1 / 3 ] ( x + 2 )
64. 2 + ( x – 1 ) ^ 5
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CH 3
pg. 261
3. – 1 – i, - 1 + i
1. 4i, - 4i
5.
-2 - 2i,
-2 + 2i
pg 277
1.
25.
x, y int = 0
26.
27.
38.
3.
X int -3, 0 , 3
y int 0
19. 3
23. 8
2 or 0 + roots
3 or 1 neg. roots
[1, 2, 3, 6, 9, 18 ]
no + roots ( no sign change )
[1, 2, 4, 12 , 13 , 2 3 , 4 3 , 16]
-3 - 9i
zero are
29. 19 + 40i
 3i and + 4
31. ( - 5 - 12i ) / 13
37. 4x^3 - 18x^2 + 14x + 12
( x-4)^2 ( x-3i)(x + 3i) = x^4 - 8 x^3 + 25 x^2 - 72x + 144
55. x = 4 , y = 0
x = 0 , y = - 12
61. HA y = ½ , VA x = -3
3
5
2  15i  6  3i 8  12i
@ 207.
=
4
4
@205.
real = 1, im =
4, 2, 0 neg roots
VA
x = -1 , HA y = 3
@206. Re 
6 3
8
real = 2
im = 3
Im 
57.
VA
x = -2, x = 4
HA y = 0
4 5
8
@208. YES …. all polynomials with real or complex coefficients have at LEAST one real / complex root….
If the exponents are all + integers

@209. y – int. ( 0, 3 / 20 )
x – int. ( 1, 0 ) ( - 3 , 0 )
VA x = 4, x = -10
HA y= 2
@210.
x – int ( -1, 0 ) ( 1 , 0 )
y-int ( 0 , 1/6 )
HA y = 1
VA x = 2, x = -3
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CH 4
pg 312
47. D: ( - inf, 0 ) R: all real , x = 0 49. D: ( 0, inf )
51. D: ( 0, inf ), R: all real , x = 0
R: all real , x = 0
PG. 338
1. see pg A28 in textbook D: all reals , R: ( 0, inf ) , y = 0
3. D: all reals R: ( - inf, 5 )
4. Domain ( - inf, inf ) Range ( 1, inf ) asymptote y = 1 graph … use GDC to verify
39.
log A + 2 log B + 3 logC
41. ½ { ln( x^2 – 1 ) - ln( x^2 + 1 ) }
42. log 4 + 3 log x - 2 log y – 5 log ( x – 1 )
62. x = ( 1/3 ) [ 5 + ( log 7 ) / ( log 2 ) ] = 2. 602452
63. 2. 303600
64. – 0. 614023
[
pg 312
47. D: ( - inf, 0 ) R: all real , x = 0
49. D: ( 0, inf )
51. D: ( 0, inf ), R: all real , x = 0
]
@211. D ( 0 , ∞ )
R ( - ∞ , ∞ ) VA x = 2
y=5
R: all real , x = 0
CH 5
E = even, O = odd…
pg 367
[[[
by the way
PG. 390
67. E * O = O
O*O=E
A = amp, p = period ,
O+O=O
68.
E*E= E
E+E = E
69.
O+ E= N
O*E= O
]]]
ps = phase shift
3. a) pi / 3
b) ( ½ , sqrt( 3 ) / 2 )
4. a) a) pi / 3 b) ( ½ , - sqrt(3) / 2 )
5. a) pi / 4
b) ( - sqrt(2) / 2 , sqrt(2) / 2 )
21. tan t = - 5/ 12 csc t = 13 / 5 sec t = -13 / 12
cot t = - 12 / 5
23. sin t = 2 / sqrt(5) cos t = - 1 / sqrt(5)
tan t = - 2 sec t = - sqrt(5)
29. A = 10, p = 4pi, ps = 0
30. A = 4, p = 1, ps = 0
32. A = 2 , p = 2pi, ps = pi / 4
37. y = 5 sin 4x
38. y = 2 sin ( ( pi / 2 ) x )
39. y = ½ sin ( 2pi ( x + 1 / 3 ) )
44. A = 1 , p = 4 pi, ps = pi
45. A = 4 , p = pi , ps = pi / 2
[ ps + means rt, ps - means left …. EX. sin ( x – pi / 4 ) means ps = + pi / 4, or pi / 4 right ]
@
212. Neither
@ 213. even
@ 214. odd
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CH 6
pg 422
angle = A
33. 1026 ft
13. x = 28 cos A ,
37. 19 ft
y = 28 sin A
14. x = 4 tan A
y = 4 sec A
PG. 449
1. a) 7pi / 18
b) 7 pi / 3
c) - 4pi/ 3
d) - 2pi / 9
3. a) 630 deg
b) - 60 deg
c) 315 deg d) 120. 3 deg or [ 378 / pi ] deg
10. A = 25 m^2
11. 18, 151 ft^2
55. 5. 32
56. 1 . 46
58. x = 9. 17
61. 77. 3 mi
63. 3. 9 mi
66. 32. 12
@ 215
@ 216 b.
138.56 ft
y9
@ 216 a.
sin x
1

cos x sin x
y
4
cos x

cos x sin x
@ 217. 71.4 mi
5. 8 m
57. 148. 07