pre-calc functions ~1~...

Pre-Calc Functions ~1~ NJCTL.org

Domain and Range

Class Work

Find the domain and range for each of the following

1. {(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.


Homework

Find the domain and range for each of the following

14. {(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 Review

Simplify each of the following

37.(𝑥4)−3 ∙ 2𝑥4 38. 2𝑥2𝑦4∙4𝑥2𝑦4∙3𝑥

3𝑥−3𝑦2 39. (2𝑥3𝑧2)

3

𝑥3𝑦4𝑧2∙𝑥−4𝑧3

Homework

Give the interval and set notation for each graph.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.


50.(𝑥−2 ∙ 𝑥−3)4 51. 6𝑥2𝑦2

3𝑥−1∙4𝑦𝑥2 52. (2𝑝𝑚−1𝑞0)

−42𝑚−1𝑝3

2𝑝𝑞2


Discrete vs. Continuous

Class Work

Is 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.


Homework

Is 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 Functions

Class Work

Is 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.


Homework

Is 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 Functions

Class Work

Let f(x)= 3x+4 and g(x)= |x-4|, find the following

105. 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)

Homework

Let f(x)= (x-1)2 and g(x)= |2x-3|, find the following

117. 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 Review

Multiply each of the following

129.(4𝑥 + 1)(2𝑥 + 6) 130. (7𝑥 − 6)(5𝑥 + 6) 131. (𝑥2 + 6𝑥 − 4)(2𝑥 − 4)

Value, Change, and Rate of Change

Class Work

Use the table below from Center for Disease Control (CDC) to answer questions 132-136. The Chart shows stature for age of males.

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?

Age (in

months)

5th

Percentile

Stature (in

centimeters)

10th

Percentile

Stature (in

centimeters)

25th

Percentile

Stature (in

centimeters)

50th

Percentile

Stature (in

centimeters)

75th

Percentile

Stature (in

centimeters)

90th

Percentile

Stature (in

centimeters)

95th

Percentile

Stature (in

centimeters)

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


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 Review

Factor each of the following

142.3𝑥2 − 2𝑥 − 5 143. 5𝑥2 + 19𝑥 + 12 144. 7𝑥2 + 53𝑥 + 28

Homework

Use 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)

10th

Percentile

Stature (in

centimeters)

25th

Percentile

Stature (in

centimeters)

50th

Percentile

Stature (in

centimeters)

75th

Percentile

Stature (in

centimeters)

90th

Percentile

Stature (in

centimeters)

95th

Percentile

Stature (in

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 Review

Factor each of the following

155.4𝑥2 − 35𝑥 + 49 156. 6𝑥2 + 7𝑥 − 49 157. 15𝑥2 − 27𝑥 − 6

Maxima and Minima Class Work 158. 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 increasing 169. Interval(s) on which f(x) is decreasing 170. x value of any local maxima 171. x value of any local minima 172. x value of any extreme max 173. x value of any extreme min 174. Interval(s) on which f(x) is concave up 175. Interval(s) on which f(x) is concave down 176. 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 9

Score 520 530 550 560 530 550 560 580 590

177. During what interval(s) were scores increasing 178. Name any relative minimum scores 179. What is the concavity of the graph at w=4 180. What was the greatest rate of change and when did it occur?


-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

x

y

Homework Use the graph of f(x) to answer the following questions. 181. Interval(s) on which f(x) is increasing 182. Interval(s) on which f(x) is decreasing 183. x value of any local maxima 184. x value of any local minima 185. x value of any extreme max 186. x value of any extreme min 187. Interval(s) on which f(x) is concave up 188. Interval(s) on which f(x) is concave down 189. 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 period

Week 1 2 3 4 5 6 7 8 9

Assignments 80 120 130 140 145 135 120 130 135

190. During what interval(s) was the number of assignments increasing 191. Name any relative minimum assignment weeks 192. What is the concavity of the graph at w=7 193. What was the greatest rate of change and when did it occur? End Behavior Class Work Use 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 +6x 198. g(x)= -5x4 -3x2 +2 199. h(x)= 2x +1 200. f(x)= 3x4 201.g(x)= 5x3 – 1


-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

x

y

-8 -6 -4 -2 2 4 6 8

-3

-2

-1

1

2

3

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

x

y

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


205.√512𝑏2 206. √80𝑝3 207. √28𝑥3𝑦3

Simplify and add each of the following

208.−2√3 + 3√27 209. 2√6 − 2√24 210. 2√6 + 3√54

Homework Use 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 +6 215.g(x)= -x6 -x2 +2 216.h(x)= 2x4 +1 217.f(x)= 6x4 +x 218.g(x)= -7x3 – x Is the graphed function odd even or neither? 219. 220. 221. Spiral Review


222.√147𝑚3𝑛3 223. √200𝑚4𝑛 224. √384𝑥4𝑦3

Simplify and add each of the following

225.−√12 + 3√3 226. 3√3 − √27 227. −3√20 − √5


Parametric Equations Class Work 228. 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 situation b. 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 + 20 y=-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 situation b. 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 + 25 y= 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 Unit Multiple 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 shoes B. amount of rain in a given week C. number of people attending a play D. the number of rotations of a wheel 5. Which of the following is a function? A. x2 + y2 = 4 B. x + y2 = 4 C. x2 + y = 4 D. 4x2 + y2 = 4 6. Given f(x) = 2(x-6)2 +2, find f(3) A. 2 B. 20 C. 29 D. 38 In Questions 7-10, refer to the graph. 7. There is a local minimum of A. -3.5 B. 0 C. 1 D. there is no local minimum 8. A point of inflection occurs at x= A. -5.5 B. -3 C. 0 D. 1 9. The rate of change from x =-2 to x=-1.5 is the same A. from x= -1 to x= 0 B. from x= 2 to x= 3 C. from x= 1 to x= 3 D. from x= .5 to x= 1 10. The graph is concave up on the domain A. (-∞,-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 is A. 3 B. .75 C. 0 D. -3 12. The greatest rate of change is between A. x= -7 and x= -6 B. x= -1 and x= 3 C. x= 1 and x= 2 D. x= 8 and x= 9 13. The rate of change from x= -5 to x= -4 is the same as the rate of change from A. x= -6 to x= -5 B. x= -3 to x= -2 C. x= 6 to x= 7 D. x= 3 to x= 5 14. In the table, the rate of change between x= 4 and x= 6 is A. 2 B. 1 C. .5 D. -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 at A. -6 B. -3 C. -1 D. 1 17. In terms of concavity, the point at x = a is A. concave up B. concave down C. a point of inflection D. 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 is A. an odd function B. an even function C. neither an odd or even function D. both an odd and even function In questions 20 and 21, consider the following parametric: 20. The initial vertical velocity is A. 4 B. 7 C. 8 D. -9 21. The position at t=3 is approximately how far from the initial position? A. 12 B. 24 C. 27 D. 36 Extended Response 1. 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 opened A. 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 notations B. 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.)


Answers 1) 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^8 38) 8x^8y^6 39) 8x^(10)z/y^4 40) {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^-20 51) xy/2 52) m^3/16p^(2)q^2 53) D 54) D 55) D

56) D 57) D 58) D 59) D 60) D 61) D 62) D 63) C, [-4,∞)

64) C, (−∞, −2] ∪ [2, ∞) 65) C, ℝ 66) D 67) D 68) D 69) D 70) D 71) D 72) D 73) D 74) D 75) D 76) C, [-6,6] 77) C, [-8,6) ∪ [−6, −4) ∪ [−4, −2) ∪ [−2,0)

78) C, ℝ 79) yes 80) no 81) yes 82) yes 83) yes 84) no 85) no 86) no 87) yes 88) no 89) yes 90) yes 91) yes 92) yes 93) no 94) yes 95) yes 96) no 97) no 98) yes 99) no 100) no 101) yes 102) no 103) yes 104) yes 105) 10 106) 13 107) 2 108) 2 109) 44 110) 1 111) 15


112) -18 113) 16 114) 1 115) |a-4| 116) 6b+4 117) 1 118) 4 119) 9 120) 1 121) 50 122) .5 123) 6 124) 9 125) 1 126) 27 127) |2a-3| 128) (2b-1)2 = 4b2-4b+1 129) 8x^2 +26x -36 130) 35x^2 +12x -36 131) 2x^3 +8x^2 -32x +16 132) 93.070608cm 133) .7299cm/mo 134) .81882cm/mo 135) .801cm/mo 136) between mo 24.5 and 25.5 137) 300 hPa 138) 27,000ft 139) –1hPa/100ft 140) -1hPa/4000ft 141) between –1hPa/200ft and -1hPa/4000ft 142) (x+1)(3x-5) 143) (x+3)(5x+4) 144) (x+7)(7x+4) 145) 91.77421cm 146) .80797cm/mo 147) .84352cm/mo 148) .88654cm/mo 149) between mo 24.5 and 25.5 150) 6 151) -1 152) 0 153) Ex: nothing happened during that time 154) between 2 and 6 155) (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 + (60

𝑏)

2

+ 𝑏

162) 12/3 inch squares 163) 27.14” by 27.14” by 27.15” 164) 56.25’ by 75’ 165) 67.604 in3

166) P=2√𝑏2 + (80

𝑏)

2

+ 𝑏

167) 1 inch squares 168) (b,d)∪ (𝑒, 𝑓) ∪ (ℎ, 𝑗) ∪ (𝑚, ∞)

169) (-∞, 𝑏) ∪ (𝑓, ℎ) ∪ (𝑗, 𝑚) 170) f & j 171) b, h, &k 172) none 173) b 174) (−∞, 𝑐) ∪ (𝑔, 𝑖) ∪ (𝑘, ∞)

175) (𝑒, 𝑔) ∪ (𝑖, 𝑘) 176) g, i, and k 177) (1,4)∪(5,9) 178) 520 and 530 179) concave down 180) -30 points/week between w=4 and w=5 181) (−∞, 𝑏) ∪ (𝑒, 0) ∪ (𝑖, ∞)

182) (𝑏, 𝑒) ∪ (0, ℎ)

183) 𝑏 𝑎𝑛𝑑 0 184) e 185) k 186) none 187) (c,f) 188) (−∞, 𝑐) ∪ (𝑓, 𝑔) 189) c and f 190) from w=1 to w=5 191) 80 and 120 192) concave up 193) 40 points/week from w=1 to w=2 194) even, neg 195) odd, neg 196) odd, pos 197) odd 198) even 199) neither 200) even 201) neither 202) odd 203) even 204) neither

205) 16b√2

206) 4p√5𝑝

207) 4xy√7𝑥𝑦

208) 7√3

209) −2√6

210) 11√6 211) odd, neg 212) even, pos 213) odd, pos 214) neither 215) even 216) even 217) neither 218) odd


219) odd 220) even 221) odd

222) 7𝑚𝑛√3𝑚𝑛

223) 10𝑚2√2𝑛

224) 8𝑥2𝑦√6𝑦

225) √3 226) 0

227) −7√5 228)a) x(t)=20t y(t)=-16t2+30t+5 b)1.441 & .434 sec c)1.69sec d)33.8ft 229) 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 sec 230) 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) B 2) D 3) D 4) C 5) C 6) B 7) C 8) D 9) D 10) B 11) B 12) A 13) D 14) C 15) C 16) D 17) A 18) B 19) C 20) C 21) 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) $27 3) A) Starts bottom left ends bottom right

B) Concave down C) Inc: (−∞, 0)

Dec: (0, ∞)

4) A) 𝑥(𝑡)30𝑡 + 2

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

pre-calc functions ~1~...

Documents