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Domain and RangeClass WorkFind the domain and range for each of the following1. {(1,2), (3,4), (5,6)}2. {(4,3), (3,2), (4,2)}3. {(5,1), (3,1), (-4,1)}

4. 5. 6.

7. 8. 9.

10. 11.

12. 13.

Pre-Calc Functions ~1~ NJCTL.org

HomeworkFind the domain and range for each of the following14. {(3,1), (-2,6), (1,4)}15. {(1,2), (2,2), (1,2)}16. {(2,1), (5,1), (-6,7)}

17. 18. 19.

20. 21. 22.

23. 24.

25. 26.


Interval and Set Notation Class Work Give the interval and set notation for each graph.27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

Spiral ReviewSimplify each of the following

37.(x4 )−3 ∙2x 4 38. 2x2 y4∙ 4 x2 y4 ∙3x

3 x−3 y239.

(2 x3 z2 )3

x3 y4 z2 ∙ x−4 z3

HomeworkGive the interval and set notation for each graph.40.

41.

42.

43.

44.

45.

46.

47.

48.

49.Simplify each of the following


50.¿ 51. 6 x2 y2

3x−1 ∙4 yx252.

(2 pm−1q0 )−42m−1 p3

2 pq2

Discrete vs. ContinuousClass WorkIs the relation discrete or continuous? If continuous, state the interval of continuity.53. {(1,2), (3,4), (5,6)}54. {(4,3), (3,2), (4,2)}55. {(5,1), (3,1), (-4,1)}

56. 57. 58.

59. 60. 61.

62. 63.

64. 65.


HomeworkIs the relation discrete or continuous? If continuous, state the interval of continuity.66. {(3,1), (-2,6), (1,4)}67. {(1,2), (2,2), (1,2)}68. {(2,1), (5,1), (-6,7)}

69. 70. 71.

72. 73. 74.

75. 76.

77. 78.


Relations and FunctionsClass WorkIs the relation a function?79. {(1,2), (3,4), (5,6)}80. {(4,3), (3,2), (4,2)}81. {(5,1), (3,1), (-4,1)}82. 83. 84.

85. 86. 87.

88. 89.

90. 91.


HomeworkIs the relation a function?92. {(3,1), (-2,6), (1,4)}93. {(1,2), (2,2), (1,2)}94. {(2,1), (5,1), (-6,7)}

95. 96. 97.

98. 99. 100.

101. 102.

103. 104.


Evaluating FunctionsClass WorkLet f(x)= 3x+4 and g(x)= |x-4|, find the following105. f(2) 106.f(3) 107.g(6)108. g(2) 109. 2f(6) 110. .5g(2)111. f(4) – g(3) 112. g(5) – f(5) 113. f(0)2

114. g(3)3 115. g(a) 116. f(2b)

HomeworkLet f(x)= (x-1)2 and g(x)= |2x-3|, find the following117. f(2) 118. f(3) 119. g(6)120. g(2) 121. 2f(6) 122. .5g(2)123. f(4) – g(3) 124. g(5) – f(5) 125. f(0)2

126. g(3)3 127. g(a) 128. f(2b)

Spiral ReviewMultiply each of the following129.(4 x+1)(2 x+6) 130. (7 x−6)(5 x+6) 131. (x2+6 x−4 )(2x−4)

Value, Change, and Rate of ChangeClass WorkUse the table below from Center for Disease Control (CDC) to answer questions 132-136.The Chart shows stature for age of males.

Age (in month

s)

5th Percentile Stature (in centimeter

s)


s)


s)


s)


s)


s)


s)

24 80.72977 81.99171 84.10289 86.4522 88.80525 90.92619 92.19688

24.5 81.08868 82.36401 84.49471 86.86161 89.22805 91.35753 92.63177

25.5 81.83445 83.11387 85.25888 87.65247 90.05675 92.22966 93.53407

26.5 82.56406 83.84716 86.00517 88.42326 90.8626 93.07608 94.40885

27.5 83.27899 84.56534 86.73507 89.17549 91.64711 93.89827 95.25754

28.5 83.98045 85.26962 87.44977 89.91041 92.41159 94.69757 96.08149

132. What is the height of a boy in the 90th percentile at age 26.5 months?133. What is the rate of change for a boy 26.5 months to 27.5 months in 25th percentile?


134. What is the rate of change for a boy 24 months to 24.5 months in 50th percentile?135. What is the average of change of a boy who is always in the 75th percentile from 24 to 28.5 months?136. At what point is a boy in the 10th percentile growing the fastest?

Use the graph of Pressure vs. Altitude to answer questions 137-141.

137. What is the pressure when the altitude is 20,000 ft?138. What is altitude when the pressure is 200 hPa?139. What is the rate of change from 20,000 ft to 40,000ft?140. What is the rate of change from 40,000ft to 60,000ft?141. What is the rate of change at 40,000ft?Spiral ReviewFactor each of the following142.3 x2−2x−5 143. 5 x2+19 x+12 144. 7 x2+53x+28

HomeworkUse the table below from Center for Disease Control (CDC) to answer questions 145-149.The chart shows stature for age of females

Age (in months

)

5th Percentile Stature (in

centimeters)


centimeters)


centimeters)


centimeters)


centimeters)


centimeters)


centimeters)

24 79.25982 80.52476 82.63524 84.97556 87.31121 89.40951 90.66355

24.5 79.64777 80.91946 83.04213 85.39732 87.74918 89.86316 91.12707

25.5 80.44226 81.73541 83.8943 86.29026 88.68344 90.83505 92.12168

26.5 81.22666 82.53699 84.72592 87.15714 89.58751 91.77421 93.08254

27.5 81.9954 83.31968 85.53389 87.99602 90.46018 92.67969 94.00873

28.5 82.74411 84.07998 86.31589 88.80551 91.30065 93.55097 94.89974

145. What is the height of a girl in the 90th percentile at age 26.5 months?


146. What is the rate of change for a girl 26.5 months to 27.5 months in 25th percentile?147. What is the rate of change for a girl 24 months to 24.5 months in 50th percentile?148. What is the average of change of a girl who is always in the 75th percentile from 24 to 28.5 months?149. At what point is a girl in the 10th percentile growing the fastest?

In Questions 150-154, refer to the graph that Cal C made of the participation of the players on the field of his soccer team. P(t) is amount of participation at any given t, time in minutes.

150. What was the amount of participation at t=7?151. What was the rate of change in participation from t =2 to t=3?152. What was the rate of change in participation from t=2 to t =5?153. What kind of false conclusion could be made from the answer in question 132?154. What is the rate of change at t=6.5?Spiral ReviewFactor each of the following155.4 x2−35 x+49 156. 6 x2+7 x−49 157. 15 x2−27 x−6

Maxima and MinimaClass Work158. An box manufacturer wants to make a box with a square base that holds 10,000 in3 and has a height of more than 1 inch. To minimize materials, what dimensions should the box have?

159. A farmer has 300’ of fence and wants to maximize the materials he has. He wants to make 2 pens the same size and that share a side. What are the dimensions of one pen?

160. A sheet of paper 8 by 10 is to have square taken out of its corners so that the remaining can be folded into a lid-less box. What is the greatest volume possible?

161. An isosceles triangle is to have an area of 30cm2. Set up an equation in terms of the base that would minimize the perimeter of the triangle.

162. A 10 by 20 sheet of material will have squares cut out of the corners and 2 squares from the middle of each long side so that when folded the net forms a jewelry box. Find the size squares to maximize the volume.

Homework


163. A box manufacturer wants to make a box with a square base that holds 20,000 in3 and has a height of more than 1 inch. To minimize materials, what dimensions should the box have?

164. A farmer has 450’ of fence and wants to maximize the materials he has. He wants to make 2 pens the same size and that share a side. What are the dimensions of one pen?165. A sheet of paper 8 by 12 is to have square taken out of its corners so that the remaining can be folded into a lid-less box. What is the greatest volume possible?

166. An isosceles triangle is to have an area of 40cm2. Set up an equation in terms of the base that would minimize the perimeter of the triangle.

167. A 10 by 8 sheet of material will have squares cut out of the corners and 2 squares of the middle of each long side so that when fold the net forms a jewelry box. Find the size squares to maximize the volume.

Increasing and Decreasing Class Work

Use the graph of f(x) to answer the following questions.

168. Interval(s) on which f(x) is increasing169. Interval(s) on which f(x) is decreasing170. x value of any local maxima171. x value of any local minima172. x value of any extreme max173. x value of any extreme min174. Interval(s) on which f(x) is concave up175. Interval(s) on which f(x) is concave down176. x value of any points of inflection

Use the table to answer the following questions. The table represents the scores one student received on practice math exams leading up to the SAT’s.Week 1 2 3 4 5 6 7 8 9Score 520 530 550 560 530 550 560 580 590

177. During what interval(s) were scores increasing178. Name any relative minimum scores179. What is the concavity of the graph at w=4180. What was the greatest rate of change and when did it occur?


Homework

Use the graph of f(x) to answer the following questions.

181. Interval(s) on which f(x) is increasing182. Interval(s) on which f(x) is decreasing183. x value of any local maxima184. x value of any local minima185. x value of any extreme max186. x value of any extreme min187. Interval(s) on which f(x) is concave up188. Interval(s) on which f(x) is concave down189. x value of any points of inflection

Use the table to answer the following questions. The table represents the number of assignments one student received in math class for a marking periodWeek 1 2 3 4 5 6 7 8 9Assignments 80 120 130 140 145 135 120 130 135

190. During what interval(s) was the number of assignments increasing191. Name any relative minimum assignment weeks192. What is the concavity of the graph at w=7193. What was the greatest rate of change and when did it occur?

End BehaviorClass WorkUse each graph to determine if the degree of the polynomial is odd or even and the sign of the lead coefficient.194. 195. 196.

Is the equation given an odd function, an even function, or neither?197 .f(x)= 3x5 +2x3 +6x198. g(x)= -5x4 -3x2 +2199. h(x)= 2x +1


200. f(x)= 3x4

201.g(x)= 5x3 – 1

Is the graphed function odd, even, or neither?202. 203. 204.

Spiral ReviewSimplify each of the following205.√512b2 206. √80 p3 207. √28 x3 y3

Simplify and add each of the following208.−2√3+3√27 209. 2√6−2√24 210. 2√6+3√54

HomeworkUse each graph to determine if the degree of the polynomial is odd or even and the sign of the lead coefficient.211. 212. 213.

Is the equation given an odd function, an even function, or neither?214.f(x)= x7 +2x3 +6215.g(x)= -x6 -x2 +2216.h(x)= 2x4 +1217.f(x)= 6x4 +x218.g(x)= -7x3 – x

Is the graphed function odd even or neither?219. 220. 221.

Spiral ReviewSimplify each of the following


222.√147m3n3 223. √200m4n 224.

√384 x4 y3

Simplify and add each of the following225.−√12+3√3 226. 3√3−√27 227. −3√20−√5Parametric EquationsClass Work228. A t-shirt cannon launches a shirt at initial vertical velocity of 30ft/sec and a horizontal velocity of 20 ft/sec. The cannon is 5 ft off the ground at the time of launch.

a. write a parametric equation to model this situationb. when is the t-shirt 15 ft above the ground?c. the person launching the shirt gets a shirt to a patron 10’ off the ground on the downward arc. How long did the shirt stay in the air?d. Considering part C, how far did the shirt travel horizontally?

229. Cal C. notices a ladybug on the window of his math classroom, considers the window to be the first quadrant, and writes a parametric equation the bug’s motion:

x= 3t + 20y=-4t + 30

a. what does each part of the equation represent?b. what direction is the bug traveling?c. If the window is 50 by 80, when does the bug reach a side and which side?

Homework

230. A t-shirt cannon launches a shirt at initial vertical velocity of 40ft/sec and a horizontal velocity of 25 ft/sec. The cannon is 4 ft off the ground at the time of launch.

a. write a parametric equation to model this situationb. when is the t-shirt 20 ft above the ground?c. the person launching the shirt gets a shirt to a patron 28’ off the ground on the downward arc. How long did the shirt stay in the air?d. Considering part C, how far did the shirt travel horizontally?

231. Cal C. notices a ladybug on the window of his math classroom, considers the window to be the first quadrant, and writes a parametric equation the bug’s motion:

x= -2t + 25y= 3t + 50

a. what does each part of the equation represent?b. what direction is the bug traveling?c. If the window is 50 by 80, when does the bug reach a side and which side?

Functions UnitMultiple Choice

1. Find the domain of {(1,3), (5,6), (6,8)}A. {1, 5, 8}B. {1, 5, 6}C. {3, 6, 8}D. Set of Reals

2. Find the range of f(x)= |x - 2| +3


A. [3, ∞]B. [1, ∞)C.(1, ∞)D. [3, ∞)

3. What is domain of the following graph? A. {x| -10< x< 10}B. {x| -10< x< 10}C. {x| -6< x< -2 or 0< x< 6}D. {x| -10< x< -4 or -2< x< 4 or 6< x< 10}

4. Which choice represents a discrete set?A. the time it takes people to tie their shoesB. amount of rain in a given weekC. number of people attending a playD. the number of rotations of a wheel

5. Which of the following is a function?A. x2 + y2 = 4B. x + y2 = 4C. x2 + y = 4D. 4x2 + y2 = 4

6. Given f(x) = 2(x-6)2 +2, find f(3)A. 2B. 20C. 29D. 38

In Questions 7-10, refer to the graph.7. There is a local minimum ofA. -3.5B. 0C. 1D. there is no local minimum

8. A point of inflection occurs at x=A. -5.5B. -3C. 0D. 1

9. The rate of change from x =-2 to x=-1.5 is the sameA. from x= -1 to x= 0B. from x= 2 to x= 3C. from x= 1 to x= 3D. from x= .5 to x= 1

10. The graph is concave up on the domainA. (-∞,-1)B. (-1, 1)C. (1, ∞)


D. (0, ∞)

In Questions 11 – 13, consider the following graph.11. The rate of change from x= 4 to x= 8 isA. 3B. .75C. 0D. -3

12. The greatest rate of change is betweenA. x= -7 and x= -6B. x= -1 and x= 3C. x= 1 and x= 2D. x= 8 and x= 9

13. The rate of change from x= -5 to x= -4 is the sameas the rate of change fromA. x= -6 to x= -5B. x= -3 to x= -2C. x= 6 to x= 7D. x= 3 to x= 5

14. In the table, the rate of change between x= 4 and x= 6 isA. 2B. 1C. .5D. -1

15. A rancher has 10,000’ of fence and wants to use it to make a pen with the maximum area. A barn 40’ by 100’ is to be used as a corner of the pen. Which equation could be used to solve this problem?A. A = 5000x – x2

B. A = 5070x – x2

C. A = 5140x – x2

D. A = 10,000x – x2

In Questions 16 – 18, refer to the graph. 16. There is a local max atA. -6B. -3C. -1D. 1

17. In terms of concavity, the point at x = a isA. concave upB. concave downC. a point of inflectionD. none of the above

18. The rate of change is positive on the interval


A. (-4 , -1.5)B. (-2, 1)C. (-1, 3)D. (1, 3)

19. Given f(x)= 24x6 +18x3 +6x2, the function isA. an odd functionB. an even functionC. neither an odd or even functionD. both an odd and even function

In questions 20 and 21, consider the following parametric: 20. The initial vertical velocity isA. 4B. 7C. 8D. -9

21. The position at t=3 is approximately how far from the initial position?A. 12B. 24C. 27D. 36

Extended Response1. The number of people entering the exciting new amusement park “MathWorld- HD in 3D” is given by the is

Where t is the amount of time after the park is openedA. If the park opened at 10am, how many entered at 1 pm?B. At what time did the park reach its maximum, assume nobody left (and who want really?)C. What is the rate of change in people entering at noon?

2. Brenda decides to save her spare change in a jar. The initial amount in the, J(0), is $20 after one week J(7)=23.50.A. How much money did Brenda save?B. At what rate is Brenda saving money?C. If Brenda’s rate of change decreases over the next week. Describe the possible effects this would have on J(14).

3. Let h(x)= 4 – 3/x

A. Describe the end behaviors of h(x) using limit notationsB. Describe the concavity of h(x)C. Describe the intervals of increase and decrease of h(x)D. For what values of x is h(x) within .01 of the limit?

4. An arrow is shot at a target with an initial vertical velocity 20’/sec and horizontal velocity of 30’/sec.The archer was standing at a line 75’ from the target, and the bow 4’ off the ground and 2’ in front of the line.


A. Write a parametric equation to model this situation.B. Where is the arrow 1 sec after launch?C. if the target has a 4’ diameter and is 2’ off the ground, does the arrow hit the target (exclude left and right of the target.)

Answers1) D:{1,3,5} R:{2,4,6}2) D:{3,4} R:{2,3}3) D:{-4, 3,5} R:{1}4) D:{-3,1,2} R:{2,5,7}5) D:{4,5,6} R:{6}6) D:{-4,0,2} R:{3,4,5}7) D:{-2,-1,2,3} R:{0,3,4,5,7}8) D:{1,2} R:{3,4,5,6}9) D:{-4,0,1,2,3} R:{5,6,7}10) D:{-4,-2,1,3} R:{0,3,4,5,7}11) D:{x>-4} R:{y>0}12) D:{x<-2 or x>2} R:{Reals}13) D:{Reals} R:{Reals}14) D:{-2,1,3} R:{1,4,6}15) D:{1,2} R:{2}16) D:{-6,2,5} R:{1,7}17) D:{-1,0,1} R:{6,7,8}18) D:{2,4} R:{6,7,8}19) D:{-5,0,5} R:{-2,-1,0}20) D:{3,4,5,6} R:{1,2,3,4}21) D:{5} R:{0,1,2,3}22) D:{3,4} R:{2,3,4}23) D:{-4,-2,2,4,5} R:{-3,2,4,5}24) D:{-6<x<6} R:{-6<y<6}25) D:{-6<x<0 } R:{-6,-2,2,4}26) D:{Reals} R:{2}27) {x|x≥1} [1,∞)28) {x|x<-3} (-∞,-3)29) {x|-2≤x≤6} [-2,6]30) {x|-3≤x<1} [-3,1)31) {x|1<x<9} (1,9)32) {x|x≤0} (-∞,0]33) {x|x≥0} [0,∞)34) {x|-8≤x≤4} [-8,4]35) {x|x>-5} (-5,∞)36) {x|4<x<10} (4,10)37) 2/x^838) 8x^8y^639) 8x^(10)z/y^440) {x|x≥-4} [-4,∞)41) {x|x<2} (-∞,2)42) {x|-5≤x≤3} [-5,3]43) {x|2≤x<6} [2,6)44) {x|-8<x<0} (-8,0)45) {x|x≤5} (-∞,5]46) {x|x≥-9} [-9,∞)

47) {x|-4≤x≤0} [-4,0]48) {x|x>2} (2,∞)49) {x|-6<x≤0} (-6,0]50) x^-2051) xy/252) m^3/16p^(2)q^253) D54) D55) D56) D57) D58) D59) D60) D61) D62) D63) C, [-4,∞ ¿64) C, (−∞ ,−2¿∪¿65) C, R66) D67) D68) D69) D70) D71) D72) D73) D74) D75) D76) C, [-6,6] 77) C, [-8,6) ∪ [−6 ,−4 )∪¿∪¿78) C, R79) yes80) no81) yes82) yes83) yes84) no85) no86) no87) yes88) no89) yes90) yes91) yes92) yes


93) no94) yes95) yes96) no97) no98) yes99) no100) no101) yes102) no103) yes104) yes105) 10106) 13107) 2108) 2109) 44110) 1111) 15112) -18113) 16114) 1115) |a-4|116) 6b+4117) 1118) 4119) 9120) 1121) 50122) .5123) 6124) 9125) 1126) 27127) |2a-3|128) (2b-1)2 = 4b2-4b+1129) 8x^2 +26x -36130) 35x^2 +12x -36131) 2x^3 +8x^2 -32x +16132) 93.070608cm133) .7299cm/mo134) .81882cm/mo135) .801cm/mo136) between mo 24.5 and 25.5137) 300 hPa138) 27,000ft139) –1hPa/100ft140) -1hPa/4000ft141) between –1hPa/200ft and -1hPa/4000ft142) (x+1)(3x-5)143) (x+3)(5x+4)144) (x+7)(7x+4)145) 91.77421cm146) .80797cm/mo147) .84352cm/mo148) .88654cm/mo149) between mo 24.5 and 25.5

150) 6151) -1152) 0153) Ex: nothing happened during that time154) between 2 and 6155) (x-7)(4x-7)156) (2x+7)(3x-7)157) (5x+1)(3x-6)158) 21.54” by 21.54” by 21.55”159) 37 1/2’ by 50’160) 52.514in3

161) P=2√b2+( 60b )2

+b

162) 12/3 inch squares163) 27.14” by 27.14” by 27.15”164) 56.25’ by 75’165) 67.604 in3

166) P=2√b2+(80b )2

+b

167) 1 inch squares168) (b,d)∪ (e , f )∪ (h , j )∪ (m,∞ )169) (-∞ ,b¿∪ ( f , h )∪( j ,m)170) f & j171) b, h, &k172) none173) b174) (−∞ ,c¿∪ ( g , i )∪ (k ,∞)175) (e ,g¿∪(i , k )176) g, i, and k177) (1,4)∪(5,9)178) 520 and 530179) concave down180) -30 points/week between w=4 and w=5181) (−∞,b )∪ (e ,0 )∪( i ,∞ )182) (b , e )∪ (0 , h)183) b∧0184) e185) k186) none187) (c,f)188) (−∞,c )∪ (f , g)189) c and f190) from w=1 to w=5191) 80 and 120192) concave up193) 40 points/week from w=1 to w=2194) even, neg195) odd, neg196) odd, pos197) odd198) even199) neither200) even


201) neither202) odd203) even204) neither205) 16b√2206) 4p√5 p207) 4xy√7 xy208) 7√3209) −2√6210) 11√6211) odd, neg212) even, pos213) odd, pos214) neither215) even216) even217) neither218) odd219) odd220) even221) odd222) 7mn√3mn223) 10m2√2n224) 8 x2 y √6 y225) √3226) 0227) −7√5228)a) x(t)=20t y(t)=-16t2+30t+5 b)1.441 & .434 sec c)1.69sec d)33.8ft229) a)3 hor. vel, 20 hor. dist from origin, -4 vert. vel, 30 vert. dist from origin. b) right and down c) bottom, 7.5 sec230) a) x(t)=25t y(t)=-16t2 + 40t + 4 b).5 & 2 sec c) 1.5 sec d) 37.5’231) a)-2 hor. vel, 25 hor. dist from origin, 3 vert. vel, 50 vert. dist from origin b) left and up c) top side, 10 sec

Review 1) B2) D3) D4) C5) C6) B7) C8) D

9) D10) B11) B12) A13) D14) C15) C16) D17) A18) B19) C20) C21) C

1) A) 39 people, B) 6th hour (4pm) 66 people, C) 6 people/hr

2) A) $3.50 B) $0.50 per day C) $273) A) Starts bottom left ends bottom right

B) Concave down C) Inc: (−∞,0) Dec: (0 ,∞ )

4) A) x (t )30 t+2 y ( t )=−16 t2+20 t+4B) 32 ft down the field, 8 ft off the groundC) No, the arrow only makes it 45 ft down the field before it hits the ground


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