NJCTLcontent.njctl.org/courses/math/pre-calculus/parent... · Web view2013/10/29 · Pre-Calc Parent Functions ~37~NJCTL.org Slope & y-intercept – Class Work Identify the slope

Slope & y-intercept – Class WorkIdentify the slope and y-intercept for each equation

1. y=3 x−4 2. y=−2x 3. y=7

4. x=−5 5. y=0 6. y−3=4(x+6)

7. y+2=−12

(x+6) 8. 2 x+3 y=9 9. 4 x−7 y=14

Write the equation of the given line in slope-intercept form and match with the correct alternate form.10. A

11. B

12. C

13. D

14. E

15. F

16. Write an equation: Cal C. drives past mile marker 27 at 11am and mile marker 145 at 1pm.

Pre-Calc Parent Functions ~1~ NJCTL.org

m=3b=−4 m=−2b=0 m=0b=7

m=undefb=¿

m=0b=0 m=4b=27

m=−12

b=−5

m=−23 b=3 m=4

7 b=−2

I. y+4=−12

( x−2 )

II. No Alternate Form(SlopeUndefined )

III. 5 x+7 y=35

IV. y−6=3 (x−4)

V. 2 x−7 y=14

VI. y−6=0 (x+2)

y=−57

x+5 III

y=0x+6 VI

y=−12

x−3 I

y=27x−2 V

y=3 x−6 IV

x=8 II

y=59 x+27

Slope & y-intercept – HomeworkIdentify the slope and y-intercept for each equation

17. y=−5x−2 18. y=3 x 19. y=−2

20. x=10 21. x=0 22. y−4=2(x−8)

23. y+3=−25

(x+10) 24. 3 x+4 y=12 25. 2 x−6 y=12

Write the equation of the given line.26. A

27. B

28. C

29. D

30. E

31. F

32. Write an equation: Cal C. drives past mile marker 45 at 11am and mile marker 225 at 2pm.


I. y+4=−4 ( x−3 )

II. x+3 y=−1

III. y+6=0(x−1)

IV. No Alternate Form(SlopeUndefined)

V. 3 x−2 y=8

VI. 2 x−9 y=2

m=0b=−2m=3b=0m=−5b=−2

m=undefb=¿

m=2b=−12

m=−25

b=−7

m=−34 b=3 m=1

3 b=−2

y=32x−4 V

y=−4 x+8 I

x=−6 IV

y=−13

x−1 II

y=29x−2 VI

y=0x−6 III

y=60x+45

Standard Form – Class WorkFind the x and y intercepts for each equation.

33. 2 x+3 y=12 34. 4 x+5 y=10

35. x−3 y=10 36. 4 x=9

37. y=0

Standard Form – HomeworkFind the x and y intercepts for each equation.

38. 3 x−5 y=15 39. 7 x+2 y=14

40. x− y=9 41. y=7

42. x=0


x : (6,0 )y :(0,4 )

x :( 52 ,0) y :(0,2)

x : (10,0 )

y :(0 ,−103

) x :( 94 ,0)

y :¿

x : infinitey :(0,0)

x : (9,0 )y :(0 ,−9)

x :¿ y :(0,7)

Horizontal and Vertical Lines – Class WorkWrite the equation for the described line

43. vertical through (1,3) 44. horizontal through (1,3)

45. vertical through (-2, 4) 46. horizontal through (-2, 4)

Horizontal and Vertical Lines – HomeworkWrite the equation for the described line

47. vertical through (4,7) 48. horizontal through (8,-10)

49. vertical through (8, -10) 50. horizontal through (4, 7)


x=1 y=3

x=−2 y=4

x=4 y=−10

x=8 y=7

Parallel and Perpendicular Lines – Class WorkWrite the equation for the described line in slope intercept form

51. Parallel to y=3 x+4 through (3,1) 52. Perpendicular to y=3 x+4 through (3,1)

53. Parallel to y=−12

x+6 through (4 ,−2) 54. Perpendicular to y=−12

x+6 through (4 ,−2)

55. Parallel to y=5 through (−1 ,−8) 56. Perpendicular to y=5 through (−1 ,−8)

Parallel and Perpendicular Lines – HomeworkWrite the equation for the described line in slope intercept form

57. Parallel to y=−2x+1 through (−6,1) 58. Perpendicular to y=−2x+1 through (−6,1)

59. Parallel to y=13x−5 through (−6,0) 60. Perpendicular to y=13

x−5 through (−6,0)


y=3 x−8 y=−13

x+2

y=−12

x y=2x−10

y=−8 x=−1

y=−2x−11 y=12x+4

y=13x+2 y=−3x−18

61. Parallel to x=5 through (−3,7) 62. Perpendicular to x=5 through (−3,7)

Point-Slope Form – Class WorkWrite the equation for the described line in point slope form.

63. Slope of 6 through (5,1) 64. Slope of -2 through (−4,3)

65. Slope of 1 through (8,0) 66. Perpendicular to y=−2x+1 through (1 ,−6)

Convert the following equations to slope-intercept form and standard form

67. y−4=5(x+3) 68. y=−2(x−1) 69. y+7=15(x−10)

Point-Slope Form – HomeworkWrite the equation for the described line in point slope form.

70. Slope of -4 through (4 ,−2) 71. Slope of 3 through (0 ,−9)

72. Slope of 1/4 through (6,0) 73. Perpendicular to y=−12

x+6 through (5 ,−2)

Convert the following equations to slope-intercept form and standard form


x=−3 y=7

y−1=6(x−5) y−3=−2(x+4)

y−0=1(x−8) y+6=12(x−1)

y=5 x+195 x− y=−19

y=−2x+22 x+ y=2

y=15x−9

x−5 y=45

y+2=−4 (x−4 ) y+9=3(x−0)

y−0=14

(x−6) y+2=2(x−5)

74. y−3=7( x−2) 75. y+1=−4 (x−7) 76. y+3=16(x−18)

Writing Linear Equations – Class WorkWrite an equation based on the given information in slope intercept form.

77. A line through (7 ,−1) and (−3,4) 78. A line through (8,2) and (6 ,−2)

79. A line perpendicular to y−7=12( x+2) through (−1 ,−8)

80. A line parallel to 4 x−6 y=10 through (9,7)

81. A function with constant increase passing through (2,3) and (8,9)

82. The cost of a 3.8 mile taxi ride cost $5.50 and the cost of a 4 mile ride costs $5.70

83. A valet parking services charges $45 for 2 hours and $55 for 3 hours


y=7 x−117 x− y=11

y=−4 x+274 x+ y=27

y=16x−6

x−6 y=36

y=−12

x+ 52 y=2x−14

y=−2x−10

y=23x+1

y=x+1

y=1.00 x+1.70

Writing Linear Equations – HomeworkWrite an equation based on the given information in slope intercept form.

84. A line through (4,9) and (−5 ,−9) 85. A line through (−8,2) and (8,2)

86. A line perpendicular to 4 x−6 y=10 through (2,2)

87. A line parallel to y−7=12( x+2) through (2,2)

88. A function with constant decrease passing through (2,3) and (8 ,−9)

89. The cost of a 3.8 mile taxi ride cost $8.25 and the cost of a 4 mile ride costs $8.75

90. A valet parking services charges $55 for 2 hours and $75 for 4 hours


y=10 x+25

y=2x+1 y=0x+2

y=−32

x+5

y=12x+1

y=−2x+7

y=2.50x−1.25

Absolute Value Functions – Class WorkGraph each function. For each, state the domain and range.

91. y=|x−4| 92. y=|2x|

93. y=|2 x−4| 94. y=2|x|

95. y=|x|+3 96. y=2|x|+3


y=10 x+35

D :R R :¿ D :R R :¿

D :R R :¿ D :R R :¿

D :R R :¿

97. y=−|x−3| 98. y=−12

|x|−3

Absolute Value Functions – HomeworkGraph each function. For each, state the domain and range.

99. y=|x+2| 100. y=|3 x|

101. y=|3x+2| 102. y=23|x|

103. y=|x|−1 104. y=23|x|−1


D :R R :¿ D :R R :¿

D :R R :¿ D :R R :¿

D :R R :¿

D :R R :¿ D :R R :¿

105. y=−|x+4| 106. y=−14

|x|+4

Greatest Integer Functions – Class WorkGraph each function. For each, state the domain and range.

107. y=[ x−4 ] 108. y=[2x ]

109. y=[2x−4] 110. y=2[x ]

111. y= [x ]+3 112. y=2 [ x ]+3


D :R R :¿

D :R R :Z D :R R :Z

D :R R :2Z

D :R R :Z D :R R :2Z+1

113. y=−[ x−3] 114. y=−12

[x ]−3

Greatest Integer Functions – HomeworkGraph each function. For each, state the domain and range.

115. y=[ x+2] 116. y=[3 x ]

117. y=[3x+2] 118. y=23[ x]

119. y= [x ]−1 120. y=23[x ]−1


D :R R : 12Z

D :R R :Z D :R R :Z

D :R R :Z D :R R : 23Z

D :R R :Z D :R R : 23Z

121. y=−[ x+4 ] 122. y=−14

[x ]+4

Identifying Exponential Growth and Decay – Class WorkState whether the given function exponential growth or decay. Identify the horizontal asymptote and the y-intercept.

123. A B

124. y=3 (4 )x 125. y=12(3)x

126. y=( 12 )x

+4 127. y=2( 14 )x

−7


D :R R :Z D :R R : 14Z

GrowthHA : y=0

y−∫ :(0,1)DecayHA : y=0

y−∫ :(0,1)

GrowthHA : y=0

y−∫ : (0,3)GrowthHA : y=0

y−∫ :(0 , 12 )

DecayHA : y=−7

y−∫ : (0 ,−5)

128. y=100 ( 13 )x

+50 129. y=17 (4 )−x

130. y=12( 34 )−x

+6 131. y=12(5)−x−2

Identifying Exponential Growth and Decay – Homework State whether the given function exponential growth or decay. Identify the horizontal asymptote and the y-intercept.

132. A B

133. y=3 ( 25 )x

134. y=5 (3)−x


DecayHA : y=50

y−∫ :(0,150)DecayHA : y=0

y−∫ :(0,17)

GrowthHA : y=6

y−∫ :(0,18)DecayHA : y=2

y−∫ :(0 ,−1 12 )

DecayHA : y=2

y−∫ : (0,3)GrowthHA : y=2

y−∫ :(0,3)

DecayHA : y=0

y−∫ : (0,3)DecayHA : y=0

y−∫ :(0,5)

135. y=6( 12 )x

+4 136. y=4 (25)x−7

137. y=100 ( 13 )− x

+50 138. y=17 (4 )x

139. y=12( 34 )x

+6 140. y=25(7)x−1

Graphing Exponentials – Class Work Graph each equation.

141. y=3 (4 )x 142. y=12(3)x

143. y=( 12 )x

+4 144. y=2( 14 )x

−7


GrowthHA : y=−7

y−∫ : (0 ,−3)

GrowthHA : y=50

y−∫ :(0,150)GrowthHA : y=0

y−∫ : (0,17)

DecayHA : y=6

y−∫ :(0,18)GrowthHA : y=−1

y−∫ :(0 ,−35 )

145. y=100 ( 13 )x

+50 146. y=17 (4 )−x

147. y=12( 34 )−x

+6

Graphing Exponentials – Homework Graph each equation

148. y=3 ( 25 )x

149. y=5 (3)−x

150. y=6( 12 )x

+4 151. y=4 (25)x−7


152. y=100 ( 13 )− x

+50 153. y=17 (4 )x

154. y=12( 34 )x

+6

Intro to Logs – Class WorkWrite each of the following in log form.

155. 102=100 156. 24=16 157. 27=33

Write each of the following in exponential form.158. log5125=3 159. log636=2 160. log7343=3


log 100=2 log216=4 log327=3

62=36 73=343

Solve the following equations161. log 464=x 162. log264=x

163. log3 y=5 164. log6 y=3

165. log b81=4 166. log b10=1

167. log5(x−2)=log5(2 x−8) 168. log 4(2 x+7)=log4 (4 x−9)

Intro to Logs – HomeworkWrite each of the following in log form.

169. 92=81 170. 25=32 171. 81=34

Write each of the following in exponential form.172. log 864=2 173. log 4256=4 174. log381=4


x=3 x=6

y=243 y=216

b=3 b=10

x=6 x=8

log 981=2 log232=5 log381=4

82=64 44=256 34=81

Solve the following equations175. log 41024=x 176. log2128=x

177. log5 y=4 178. log7 y=4

179. log b1000=3 180. log b1024=10

181. log5(x+2)= log5(3x−8) 182. log 4(3 x−6)= log4(x+10)

Properties of Logs – Class WorkUsing Properties of Logs, fully expand each expression

183. log 4 x y3 z4 184. log6wx2 y

185. log77m2

(uv )2

Using log25≈2.3219 and log210≈3.3219, evaluate the following186. log250 187. log2100 188. log220


x=5 x=7

y=2401

b=2

x=5 x=8

log 4 x+3 log 4 y+4 log4 z

log6w−2 log6 x−log6 y

1+2 log7m−2( log7u+ log7 v)

6.6438 4.3219

Using Properties of Logs, rewrite the expression as a single log.189. log x+log y−log z 190. 1−3 log5m 191. 5 log k−3( logr+ log t )

Solve the following equations192. log3 x+ log34=5 193. log2 x+ log2(x+3)=2

194. log3 x+12log34=

14log316 195. log3 x+ log3(x−2)=log335

196. 2 log3 x−log34= log316 197. log3(x+3)+log3(x−2)=log366

Properties of Logs – Home WorkUsing Properties of Logs, fully expand each expression

198. log33 x y2 z5 199. log 44wx2

200. log 88m4

(u2 v )3

Using log23≈1.5850 and log218≈4.1699, evaluate the following


log xyz log5

5m3

log k5

(rt )3

x=60.75 x=1

x=7

x=8

1+log3 x+2 log3 y+5 log3 z

1+log 4w−2 log4 x

1+4 log8m−3(2 log8u+ log8 v)

201. log216 202. log236 203. log281

Using Properties of Logs, rewrite the expression as a single log.204. 2 log x+3 log y−4 log z 205. 1−2 log 4m 206. 5 log f −2 log g−6 logh

Solve the following equations207. log34 x+ log32=3 208. log2 x+ log2 (x−3 )=2

209. log3 x−log34=log316 210. log3 x2+ log3 x=log327

211. 2 log3 x−log39=log325 212. log3(2x+3)+ log3(x−2)=log372

Common Logs – Class WorkSolve for the variable.

213. 7x=18 214. 3x+4=27x 215. 4b−2=8


−2.5849 5.1699 6.34

log x2 y3

z4 log 4

4m2 log f 5

g2h6

x=3.375 x=4

x=3

x=15 x=6.5

x= log 18log 7

≈1.485 x=2 b= log 8log 4

+2≈3.5

216. 52d−3=29 217. 7n−2=3n 218. 4 t+2=5t−2

Find the approximate value for each219. log36 220. log517 221. log637

Common Logs – Home Work Solve for the variable.

222. 8x=21 223. 64x−1=42 x+5 224. 9b−6=42

225. 193d−1=40 226. 25−n=7n 227. 18t+1=32t−1

Find the approximate value for each228. log310 229. log520 230. log630

e and ln – Class WorkSolve the following equations

231. e ln x=6 232. e ln x−4=6 233. ln e x+5=6 x


n= 2 log7log7−log3

≈4.593 t=2 log5+2 log 4log5−log 4

≈26.85

1.6309 1.7604 2.0153

x=8 b= log 42log 9

+6≈7.701

t= log 32+log 18log 32−log18

≈11.047

2.0959 1.8614 1.8982

x=10 x=1

234. 3 ln e2x−8=4 235. e2x=7 236. 3e( x−1)+9=10

237. ln ( x+1 )=7 238. ln (x¿)+1=7¿

e and ln – HomeworkSolve the following equations

239. e ln 2 x=6 240. 5e ln x−4=6 241. ln e2x−5=6+x

242. 4 ln e3x+9=21 243. e3x+1=6 244. 4 e(2x+1 )+8=10

245. ln ( x−1 )=9 246. ln (x¿)−1=9¿

Growth and Decay – Class WorkSolve the following problems

247. $250 is deposited in an account earning 5% that compounds quarterly, what is the balance in the account after 3 years?


x= ln 72

≈0.973 x=ln 13−1≈−2.099

x=e7−1≈1095.633 x=e6≈403.429

x=2 x=11

x=ln 12−1

2≈−0.847

$290.19

248. A bacteria colony is growing at a continuous rate of 3% per day. If there were 5 grams to start, what is the mass of the colony in 10 days?

249. A bacteria colony is growing at a continuous rate of 4% per day. How long till the colony doubles in size?

250. If a car depreciates at an annual rate of 12% and you paid $30,000 for it, how much is it worth in 5 years?

251. An unknown isotope is measured to have 250 grams on day 1 and 175 grams on day 30. At what rate is the isotope decaying? At what point will there be 100 grams left?

252. An antique watch made in 1752 was worth $180 in 1950; in 2000 it was worth $2200. If the watch’s value is appreciating continuously, what would its value be in 2010?

253. A furniture store sells a $3000 living room and doesn’t require payment for 2 years. If interest is charged at a 5% daily rate and no money is paid early, how much money is repaid at the end?

Growth and Decay – HomeworkSolve the following problems

254. $50 is deposited in an account that earns 4% compounds monthly, what is the balance in the account after 4 years?


6.75 grams

17.33days

$15,831.96

r=0.012=1.2%77.07days

$3,629.55

$3,315.49

$58.66

255. A bacteria colony is growing at a continuous rate of 5% per day. If there were 7 grams to start, what is the mass of the colony in 20 days?

256. A bacteria colony is growing at a continuous rate of 6% per day. How long till the colony doubles in size?

257. If a car depreciates at an annual rate of 10% and you paid $20,000 for it, how much is it worth in 4 years?

258. An unknown isotope is measured to have 200 grams on day 1 and 150 grams on day 30. At what rate is the isotope decaying? At what point will there be 50 grams left?

259. An antique watch made in 1752 was worth $280 in 1940; in 2000 it was worth $3200. If the watch’s value is appreciating continuously, what would its value be in 2010?

260. A $9000 credit card bill isn’t paid one month, the credit company charges .5% continuously on unpaid amounts. How much is owed 30 days later? (assume no other charges are made)

Logistic Growth – Class WorkScientists measure a wolf population growing at a rate of 3% annually. They calculate the carrying capacity of the region to be 100 members.

261. Write a logistic equation to model this situation.


r=0.0096=0.96%144.57days

Pt+1=Pt+0.03P t(1−Pt

100)

262. Create a table that shows the pack population over the next 10 years if P1=30

263. Draw a graph of the equation

Logistic Growth – HomeworkA calculus class determines that a rumor spreads around the school at a rate of 15% per hour. The school population is 1600.

264. Write a logistic equation to model this situation.

265. Create a table that shows the number of people who know the rumor over the next 10 hours if the class that starts it has 20 members

266. Draw a graph of the equation

Trig Functions – Class WorkUse the appropriate triangle to answer questions 267-274.

267. sin θ=¿¿ 268. cosθ=¿


Pt+1=Pt+0.15P t(1−Pt

1600)

1819.5

≈0.923 7.519.5

≈0.385

269. tanθ=¿ 270. sin α=¿

271. cos α=¿ 272. tan α=¿

273. θ=¿ 274. α=¿

275. A right triangle has a hypotenuse of 7 and an angle of40 °, find the larger leg.

276. A right triangle has legs of 6 and 10 find the smaller acute angle.

277. A right triangle has an angle of 50 ° and a longer leg of 8, find the hypotenuse.

Trig Functions – HomeworkUse the appropriate triangle to answer questions 278-285.

278. sin θ=¿¿ 279. cosθ=¿


187.5

≈2.4 10.517.5

≈0.6

10.514

≈0.75

36.87 °

5.36

30.964 °

10.44

817

≈0.471 1517

≈0.882

280. tanθ=¿ 281. sin α=¿

282. cos α=¿ 283. tan α=¿

284. θ=¿ 285. α=¿

286. A right triangle has a hypotenuse of 9 and an angle of60 °, find the larger leg.

287. A right triangle has legs of 7 and 12 find the smaller acute angle.

288. A right triangle has an angle of 20 ° and a longer leg of 5, find the hypotenuse.

Converting Degrees and Radians – Class workConvert the following degree measures to radians and radian measures to degrees.

289.2π3 290. 35 ° 291. 225 °


815

≈0.533 1620

≈0.8

1612

≈1.333

28.07 ° 53.13 °

7.794

30.256 °

5.321

120 ° 7π36 5π

4

292.π5 293. 150 ° 294.

14π9

295. 310 ° 296. 10π7 297. 270 °

Converting Degrees and Radians – Class workConvert the following degree measures to radians and radian measures to degrees.

298.5π3 299. 75 ° 300. 200 °

301.4 π5 302. 175 ° 303.

17π9

304. 350 ° 305. 9π7 306.

11π18

Graphing Sin, Cos, and Tan – Class Work


31π18 257.14 ° 3π

2

340 °

231.43 ° 110°

10π9

35π36

35π18

305. What is the relationship between when a sine max/min value occurs and when a cosine zero occurs?

306. How do the zeros of the cosine and sine graphs relate to a tangent graph?

Consider the domain of (– π ,π ) for sin θ ,cosθ ,∧tan θ307. Which function(s) is increasing on the entire interval?

308. Which function(s) has a relative max?

309. Which function(s) has a concave down interval followed by a concave up interval?

310. Which function(s) has an undefined value of x on the interval?

Graphing Sin, Cos, and Tan – Homework311. What is the relationship between when a cosine max/min value occurs and when a sine zero occurs?

312. How does the tangent function’s concavity change between asymptotes?

Consider the domain of (– π ,π ) for sin θ ,cosθ ,∧tan θ313. Which function(s) is decreasing on the entire interval?

314. Which function(s) has a zero?

315. Which function(s) has a concave up interval followed by a concave down interval?

316. Which function(s) has a relative minimum?

Positive and Negative Integer Power Functions – Class Work


A sine max/min occurs at the exact same x-value as cosine zeros.

The sine zeros are where tangent also has zeros. The cosine zeros are where tangent has vertical asymptotes.

tan x

sin x ,cos x

cos x , tan x

tan x

A cosine max/min occurs at the exact same x-value as sine zeros.

Tangent is concave down, then changes to concave up between the vertical asymptotes.

¿

sin x ,cos x , tan x

sin x , tan x

sin x ,cos x

For each equation find limx→−∞

❑, limx→0−¿ f (x) , lim

x→0+¿ f (x) ,∧limx→∞

f (x)¿¿¿

¿.

317. f ( x )=4 x3 318. f ( x )=5 x6

319. f ( x )=−13

x5 320. f ( x )=−x2

321. f ( x )=4 x−3 322. f ( x )=5 x−6

323. f ( x )=−13

x−5 324. f ( x )=−x−2


limx→−∞

f (x )=−∞

limx→ 0−¿ f ( x )=0¿

¿ limx→ 0+¿ f (x )=0¿

¿

limx→∞

f (x)=∞

limx→−∞

f (x )=∞

limx→ 0−¿ f ( x )=0¿

¿ limx→ 0+¿ f (x )=0¿

¿

limx→∞

f (x)=∞

limx→−∞

f (x )=−∞

limx→ 0−¿ f ( x )=0¿

¿ limx→ 0+¿ f (x )=0¿

¿

limx→∞

f (x)=−∞

limx→−∞

f (x )=0

limx→0−¿ f ( x )=−∞¿

¿

limx→ 0+¿ f (x )=∞¿

¿ limx→∞

f (x)=0

limx→−∞

f (x )=0 limx→ 0−¿ f ( x )=∞¿

¿

limx→ 0+¿ f (x )=∞¿

¿limx→∞

f (x)=0

Positive and Negative Integer Power Functions – Homework

For each equation find limx→−∞

f (x) , limx→0−¿ f (x) , lim

x→0+¿ f (x) ,∧limx→∞

f (x)¿¿¿

¿.

325. f ( x )=3 x9 326. f ( x )=−2x8

327. f ( x )=−14

x11 328. f ( x )=6x20

329. f ( x )=3 x−9 330. f ( x )=−2x−8

331. f ( x )=−14

x−11 332. f ( x )=6x−20


limx→−∞

f (x )=−∞

limx→ 0−¿ f ( x )=0¿

¿ limx→ 0+¿ f (x )=0¿

¿

limx→∞

f (x)=∞

limx→−∞

f (x )=−∞

limx→0−¿ f ( x )=0¿

¿ limx→ 0+¿ f (x )=0¿

¿

limx→∞

f (x)=−∞

limx→−∞

f (x )=∞

limx→0−¿ f ( x )=0¿

¿ limx→ 0+¿ f (x )=0¿

¿

limx→∞

f (x)=∞

limx→−∞

f (x )=0

limx→0−¿ f ( x )=−∞¿

¿

limx→ 0+¿ f (x )=∞¿

¿ limx→∞

f (x)=0

limx→−∞

f (x )=0

limx→0−¿ f ( x )=−∞¿

¿

limx→0+¿ f (x )=−∞¿

¿

limx→∞

f (x)=0

limx→−∞

f (x )=0 limx→ 0−¿ f ( x )=∞¿

¿

limx→0+¿ f (x )=−∞¿

¿

limx→∞

f (x)=0

limx→−∞

f (x )=0 limx→ 0−¿ f ( x )=∞ ¿

¿

limx→0+¿ f (x )=∞¿

¿limx→∞

f (x)=0

Rational Power Functions – Class WorkChoose which function(s) fits the description provided.

(A) f ( x )=x13 (B) f ( x )= 4√x (C) f (x)=x

16 (D) f ( x )= 7√x

333. undefined for negative real values 334. limx→−∞

f (x )=−∞

335. closest to (10,1) 336. limx→0+¿ f (x )=0¿

¿

337. limx→ 0−¿ f ( x )=undefined¿

¿ 338. closest to (10 , 3)

Rational Power Functions – HomeworkChoose which function(s) fits the description provided.

(A) f ( x )=−x13 (B) f ( x )=−4√x (C) f ( x )=−x

16 (D) f ( x )=−7√x

339. Domain is (−∞,∞) 340. limx→∞

f (x )=∞


B and C A and D

D A, B, C, and D

B and C A

A and D None

341. closest to (5,-1.5) 342. limx→0

f ( x )=undefined

343. Range is ¿ 344. closest to (10 ,- 1.5)

Rational Functions – Class WorkFor each of the following functions, name any discontinuities and tell whether they are non-removable or removable. Graph each function.

345. h(x )=3 x2−4 x−4x2−4

346. g ( x )= x−5x2−25

347. j ( x )= x2−12x+36x−6

348. m (x )= x2−9x2−6 x+9


B B and C

B and C C

x=2 removablex=−2 non-removable


x=3 non-removable

349. limx→ 3−¿ f (x)= lim

x →3+¿f ( x)=2 ;f (3) isundefined ¿¿ ¿

¿

Rational Functions – HomeworkFor each of the following functions, name any discontinuities and tell whether they are non-removable or removable. Graph each function.

350. h(x )= x2−4 x+4x2−4

351. g ( x )= x−4x2−16

352. j ( x )=2x2−8x−24x−6

353. m (x )= x2−49x2+14 x+49


x=3 removable

Graphs will vary.Any graph that would go through the point (3,2), but instead has a

hole at that point.



x=−7 non-removable

354. limx→−5−¿ f (x)= lim

x→−5+ ¿ f (x)=1; f (−5) isundefined ¿¿ ¿

¿

Unit Review - Multiple Choice

1. Which equation has an x-intercept of (5,0) and a y-intercept of (0 ,−52)

a. y+ 52=5(x−0)

b. y−52=5( x−0)

c. y=12(x−5)

d. y=12(x+5)

2. The equation of a line perpendicular to 2 x+3 y=7 and containing (5,6) isa. 3 x−2 y=3

b. y−6=−23

(x−5)

c. 3 x−2 y=4

d. y=23(x−6)

3. A line with no slope and containing (3,8) has equationa. y=3b. y=8c. x=3d. x=8

4. The vertex of y=−2|x−1|+7 isa. (2,7)b. (−2,7)


x=−5 removable

Graphs will vary.Any graph that would go through

the point (−5,1), but instead has a hole at that point.

C

A

B

D

c. (−1,7)d. (1,7)

5. 4 [−3 (2.7 )+0.5 ]=¿a. −40b. −36c. −32d. −28

6. The equation that models exponential decay passing through (0,5) and a limx→∞

f (x )=4 is

a. f ( x )=5 ex+4b. f ( x )=−1e x+4c. f ( x )=5 e−x+4d. f ( x )=−1e− x+4

7. A forest fire spreads continuously, burning 10% more acres every hour. How long will it take for 1000 acres to be on fire after 200 acres are burning?

a. 23.026 hoursb. 16.094 hoursc. 6.932 hoursd. not enough information

8. log65=¿a. .116b. .898c. 1.113d. 1.308

9. Given 4 x=10, find xa. 2.5b. .602c. .400d. 1.661

10. logm=.345∧log n=1.223, find log 10m2

n3

a. -1.979b. .651c. 6.507d. 8.473

11. Which of the following would not influence the carrying capacity of a logistic growth modela. the population of a townb. the food supply in an ecological preserve


C

D

B

B

D

A

C

c. the rate of spread of the flud. the area inside a Petri dish

12. The larger leg of a right triangle is 6 and the smallest angle is 20°, what is the hypotenuse?a. 6.385b. 5.638c. 17.543d. 14.703

13. How many degrees is 4 π9

?

a. 160°b. 110°c. 80°d. 62°

14. An example of a function that is concave down and then concave up isa. f ( x )=sin x on(0 , π )b. f ( x )=tan xon (0 , π )c. f ( x )=cos xon (0 , π )d. f ( x )=sin x on(−π , π)

15. The function that has limx→ 0−¿ f ( x )=∞∧ lim

x→0+¿ f ( x )=−∞ ¿¿ ¿

¿ is

a. f ( x )=−3x3

b. f ( x )=−4 x4

c. f ( x )=−3x−3

d. f ( x )=−4 x−4

16. The function h ( x )=4 x2−3 x−14 x2−1

has the following discontinuities

a. non-removable discontinuity at x=± 12

b. removable discontinuity at x=± 12

c. non-removable discontinuity at x=12 ; removable discontinuity at x=−12

d. non-removable discontinuity at x=−12 ; removable discontinuity at x=12

Extended Response

1. Consider the function h ( x )= f (x )g (x)

, if f ( x )=x2−2x−8 and g ( x )=x2+8x+15

a. Use limit notation to describe the end behavior of h(x )


A

C

C

C

A

limx→−∞

h ( x )=+1limx→∞

h ( x )=+1

b. Name any discontinuities and whether they are removable or non-removable.

c. j ( x )=h (x) ∙m (x ) and has a removable discontinuity at x=−3,what is m(x)?

2. Entomologists introduce 20 of one variety of insect to a region and determine that the population doubles every 6 hours.

a. Write an equation to model this situation.

b. What will the population be in 10 hours?

c. If those same scientists determine that the region can support a maximum of 100,000 of the species, rewrite your equation from part a.

3. A compostable bag breaks down such that only 10% remains in 6 months.a. If the decomposition is continual, at what rate is the bag decomposing?

b. How much of the bag remained after 4 months?


x=−5 ,−3both non−removable

A=20 e0.1155 t

63.48hours

Pt+1=Pt+0.1155Pt(1−Pt

100000)

r=38.4%decay per month

21.5%remaining

c. When will there be less than 1% of the bag remaining?

4. A 15’ ladder is rated to have no more than a 70° angle and no less than a 40° angle.a. What is maximum rated distance the ladder can be placed from the wall?

b. How high up a wall can the ladder reach and be within the acceptable use limits?

c. At what base angle should the ladder be placed to reach 10’ up the wall?


after 12months

11.5 feet

14.1 feet

41.8 °

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NJCTLcontent.njctl.org/courses/math/pre-calculus/parent... · Web view2013/10/29 · Pre-Calc Parent Functions ~37~NJCTL.org Slope & y-intercept – Class Work Identify the slope