FunctionsGraphingClass WorkMatch the equation with its graph.

1. y=ln x A B C2. y=4 x2−5

3. y= 5x+2

4. y=√25−( x−3 )2D E F5. y=−2x3

6. y=−2x7. y=4e x−8 G H J8. y=5−|4+x|9. – y=|x−4|−510. y=x3−4 x2+6 x−8K L M11. y=x2

12. y=1

4−x2

13. y=−√5−x N P Q

14. y=4x−2

15. y=3cos ( x )HomeworkMatch the equation with its graph.

16. y=lnx+2 A B C17. y=ln ( x+2 )18. y=|ln x|19. y=|√x−2| D E F20. y=e−x

21. y=e|x|

22. y=5sin x G H J23. y=sin2x+cos2x

24. y=x+2x2−4

25. y=1x K L M

26. y=−3cos x27. y=x2

60

65

70

75

80

85

90

95

100

105

110

25 30 35 40 45 50 55 60

Time spent studying

test

sco

res

5:55

7:07

8:19

9:31

10:43

11:55

0 5 10 15 20 25

Time spent training

Mile

tim

e

28. y=44+x2

N P Q

29. y=−130. y=−e−x

Slopes and EquationsClass Work

31. What is the slope of the line through M(2, -3) and N(4, -1)?32. Write the equation of the line through M(2, -3) and N(4, -1) in slope-intercept form.33. Write the equation of the line through M(2, -3) and N(4, -1) in point-slope form.34. Write the equation of the line through M(2, -3) and N(4, -1) in standard form.35. Write the equation of the line through (4, 5) and parallel to y -6=2(x+5).36. Write the equation of the line through (4, 5) and perpendicular to y -6=2(x+5).37. 3x - y=5 and y - 6 = a(x+6) are perpendicular, find a.38. Use the table at the right to answer the following:

a. Write a prediction equation for the data.b. What does slope mean in your equation?c. Predict what grade comes from studying

45 minutes?d. How long would you need to study for a 100?

Homework39. What is the slope of the line through M(5,0) and N(4, -6)?40. Write the equation of the line through M(5,0) and N(4, -6) in slope-intercept form.41. Write the equation of the line through M(5,0) and N(4, -6) in point-slope form.42. Write the equation of the line through M(5,0) and N(4, -6) in standard form.43. Write the equation of the line through (8,2) and parallel to y - 7=3(x - 5).44. Write the equation of the line through (4, 5) and perpendicular to y - 7=3(x - 5).45. 4x - 2y=5 and 2x + ay = 7 are perpendicular, find a.46. Use the table at the right to answer the following:

a. Write a prediction equation for the data.b. What does slope mean in your equation? c. Predict what time comes from training

6 hours?d. How long would you need to train to be

7 minutes?

Relations, Functions, and Their GraphsClass WorkState the domain and range for the following. Find when f(x)=0. Graph the function.

47. f (x)=√3 x+4+1348. f (x)=|5 x+2|+4

49. f (x)= x+25 x−10

50. f (x)= 41−x

51. f (x)=12ex

Is the following function an odd-function, an even-function or neither.52. f ( x )=5 x4−6 x2+3 x53. y=5 x5−3 x3+1x54. g ( x )=2 x2 (4 x3−3x )

55. h ( x )=45x2+2

56. Use the piecewise function at right to answer the following:a. f(-2)b. f(0)c. f(4)d. state the domain and range of fe. graph f

57. Use the piecewise function at right to answer the following:a. f(-2)b. f(2)c. f(4)d. state the domain and range of fe. graph f

58. Write a piecewise function for the graph.

HomeworkState the domain and range for the following. Find when f(x)=0. Graph the function.

59. f (x)=√5−2 x+760. f (x)=|3 x−2|−4

61. f (x)=2 x−14−x

62. f (x)= 2x+1

63. f (x)=4+ ln xIs the following function an odd-function, an even-function or neither.

64. f ( x )=2x4+3 x2−265. y=5 x5−3 x+166. g ( x )=2 x (4 x2−3x )

67. h ( x )=4 x68. Use the piecewise function to answer the following.

a. f(-2)b. f(1) c. f(4)d. state the domain and range of fe. graph f

69. Use the piecewise function to answer the following.a. f(-2) b. f(2)c. f(4)d. state the domain and range of fe. graph

70. Write a piecewise function for the graph.

Exponential FunctionsClass WorkGraph the following functions. State the domain and range for each. Find any zeros.

71. y=ex−672. f ( x )=−2e−x

73. y=6−3ex

74. f ( x )=.5 e−x

75. y=2x−176. Write equations for the following graphs. (Each has base e.) Window is [-5,5] by [-5,5]A. B. C.

77. $250 is deposited in an account earning 5% that compounds quarterly, what is the balance in the account after 3 years?

78. 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?

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

80. 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?

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

82. 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?

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

HomeworkGraph the following functions. State the domain and range for each. Find any zeros.

84. y=4x+285. f ( x )=−2+e−x

86. y=5−2ex

87. f ( x )=−.5e−x

88. y=3x−289. Write an equation for the following graphs. (Each has base e.) Window is [-5,5] by [-5,5]A. B. C.

90. $50 is deposited in an account that earns 4% compounds monthly, what is the balance in the account after 4 years?

91. 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?

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

93. 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?

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

95. 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?

96. 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)

TransformationsClass Work

In each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) determine the domain and range, and (iv) draw the graph of both.97. h ( x )=4(−x+3)2+6

98. h ( x )= 3(2 x+1)

−2

99. h ( x )=2√3−x+4

100. h ( x )=2|3 x−6|−1101. h ( x )=3e−2x+4The graph at right is the graph of f(x). Draw the graphs of the h(x).102. h ( x )=f (− x)103. h ( x )=−f ( x)104. h ( x )=2 f ( x+3 )105. h ( x )=−2 f (1− x )+3

HomeworkIn each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) determine the domain and range, and (iv) draw the graph of both.

106. h ( x )=4(2 x−3)13+2

107. h ( x )= 3(x−2)2

−4

108. h ( x )=2cos(2 x− π2 )−3109. h ( x )=−tan(−12 x)+1110. h ( x )= log (2−x )+4The graph at right is the graph of f(x). Draw the graphs of h(x).111. h ( x )=f (− x)112. h ( x )=−f ( x)113. h ( x )=3 f ( x+2 )114. h ( x )=−3 f (2−x )+2

Solving Equations and InequalitiesClass WorkSolve algebraically.

115. x2−6 x+8=0116. 3 x3−27=0117. 10 x2−14 x=0118. 4<5− y<10119. |x−3|=5120. |4−x|>3

Solve graphically.121. x4−5x3+4 x2−6 x+7=0122. −2 x4+3 x3−3 x2+8 x≤0123. A farmer wants to make 2 pens with 800 ft of fencing. The pens will share a common

side. What are the dimensions of one pen that maximize the fence?

124. A gardener wants to pen in a garden using her house as one side. The garden is to be 200 sq ft. How much fence is needed if the gardener is trying to minimize the fence?

125. An open top box is formed by cutting the same size square out of each corner of a rectangular piece of material. If the sheet is 8m by 10m. What is the maximum volume possible?

126. A pizza box is created by cutting 6 equal squares out of the corners and the middles of the two longest sides of a 20” by 50” piece of cardboard. What is the largest diameter pizza when the box is maximized for volume?

HomeworkSolve algebraically.

127. x2−8 x−20=0128. 2 x2−20=0129. 12 x3−6 x=0130. −2<6−2 y<8131. 2|x+4|=8132. |3−2 x|>15

Solve graphically.133. 3 x4−2 x3+5x2−2x+1=0134. −x4+4 x3−2 x2+4≥0135. A farmer wants to make 2 pens with 600 ft of fencing. The pens will share a common

side. What are the dimensions of one pen that maximize the fence?136. A gardener wants to pen in a garden using 10’ of her house as part of one side. The

garden is to be 400 sq ft. How much fence is needed if the gardener is trying to minimize the fence?

137. An open top box is formed by cutting the same size square out of each corner of a rectangular piece of material. If the sheet is 14m by 8m. What is the maximum volume possible?

138. A pizza box is created by cutting 6 equal squares out of the corners and the middles of the two longest sides of a 30” by 70” piece of cardboard. What is the largest diameter pizza when the box is maximized for volume?

Relations, Functions, and Their InversesClass WorkGiven f(x), find f-1(x). Show that f(f-1(x)) = f-1(f(x)) = x. Graph f(x) and f-1(x) on the same graph. Describe the domain and range for f -1(x).

139. f ( x )=3 x−2140. f ( x )=2 x2+1

141. f ( x )=1−x23

142. f ( x )=4−x−3

143. f ( x )=4+ ln x144. ln y=3x−2

145. y+ ln 4=ln x−6

HomeworkGiven f(x), find f-1(x). Show that f(f-1(x)) = f-1(f(x)) = x. Graph f(x) and f-1(x) on the same graph. Describe the domain and range for f -1(x).

146. f ( x )=5 x+2

147. f ( x )=23x2−6

148. f ( x )=9x25

149. f ( x )=5−3 x−2

150. f ( x )=2 ln x+1151. y+3=ln x−6152. y−ln 12=ln (4 x )−8

TrigClass WorkFind the exact value of the given expression.

153. cos 4 π3

154. sin 7π4

155. sec 2π3

156. tan−5 π6

157. cot 15π4

158. csc−9π2

159. Given the terminal point ( 37 ,−2√107 ) find tanθ160. Given the terminal point (−513 ,−1213 ) find cotθ161. Knowing cosx=

23and the terminal point is in the fourth quadrant find sinx.

162. Knowing cotx=45and the terminal point is in the third quadrant find secx.

State the amplitude, period, phase shift, and vertical shift for each function. Draw the graph by hand and then check it with a graphing calculator.

163. y=2cos (2(x+ π3 ))+1164. y=−3cos (4 x−π )−2

165. y=sin( 23 ( x+ π6 ))+3166. y=−1cos (3 x−2 π )−1

167. y=23cos (4 x−2π )+2

Evaluate the expression.

168. sin(cos−1 513 )169. cos (tan−1−6

5 )170. tan(sin−1 3

4 )171. sin( tan−1− 7

13 )172. cos (sin−1 6

11 )HomeworkFind the exact value of the given expression.

173. cos 5π3

174. sin 3π4

175. sec 4 π3

176. tan−7 π6

177. cot 13π4

178. csc−11π2

179. Given the terminal point ( 725 ,−2425 ) findcotθ180. Given the terminal point (−4 √2

9, 79 ) find tanθ

181. Knowing sinx=78and the terminal point is in the second quadrant find secx.

182. Knowing cscx=−45 and the terminal point is in the third quadrant find cotx.

State the amplitude, period, phase shift, and vertical shift for each function. Draw the graph by hand and then check it with a graphing calculator.

183. y=−4cos (12 ( x− π3 ))+2184. y=−2cos (4 x−3 π )−3

185. y=2sin( 14 (x+ π2 ))+1186. y=−1cos (6x−2π )−1

187. y=32cos (4 x−3π )−2

Evaluate the expression.

188. sin(cos−1 1213 )189. cos (tan−1−7

5 )190. tan(sin−1 1

4 )191. sin( tan−1− 5

13 )192. cos (sin−1 9

11 )Parametric EquationsClass Work193. 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?

194. 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 + 30a. 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

195. 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?

196. 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 + 50a. 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?

Multiple ChoiceWithout a Calculator

1. Which of the following is undefined at x=2?

a. y= x2−4 x+4x2−2

b. y=√2−xc. y=|x2−4|d. y=ex−2

e. y=cos−1 x2. What is the equation of the line through (2,6) and perpendicular to 2x +3y=7?

a. y=−23x+ 22

3

b. y=32x−3

c. y−6=32

( x−2 )

d. 2 x+6 y=7e. 3 x−2 y=−6

3. Which of the following graphs is symmetric to the origin?a. f ( x )=3 x−1b. g ( x )=5 x5−3 x3+7

c. h ( x )= 5x−3

d. y= 3√xe. y=4 x4+2 x2−6

4. If f ( x )=16−x2 and g ( x )=√4−x , find h(x) if h(x)=( f ° g (x ) )a. 0

b. 12−xc. 12−x2

d. 12+xe. 12+x2

5. The function y=|sinx−2|has the maximum value ofa. -2

b.π2

c.3π2

d. 2e. 3

6. The zero for g ( x )=−2 x3+4 x+6 is betweena. -2 and -1b. -1 and 0c. 0 and 1d. 1 and 2e. 2 and 3

Calculator Permitted7. The prediction equation of C(x)= .2x + 4 for a taxi ride where C is the cost and x

is in tenths of a mile. What is the predict cost of a 3 mile ride?a. $4.23b. $4.60c. $6d. $10

8. Which of the following equations is symmetric to the y-axis?

a. y= 1x2−4

b. f ( x )=3 x4−6 x2−8c. g ( x )=√2−x2d. h ( x )=sin x

9. The function g ( x )=3 x3−10 x2−23 x−10 has how many zero(s)?a. 0b. 1c. 2d. 3e. 4

10.The inverse of f ( x )=ex−2 isa. f−1 (x )=ln ( x−2 )

b. f−1 (x )=ln ( x+2 )c. f−1 (x )=ln ( x )−2d. f−1 (x )=ln x+2e. f−1 (x )=ln|x|−2

11.sin (arctan1 )=¿a. 0

b.12

c. √22

d. √32

e. 112. If f(x) is an odd function, which of the following must be true?

a. f(x) = f(-x)b. f(x) = -f(x)c. f(-x) = -f(x)d. f-1(x) = f(x)e. f-1(x) = f(-x)

In questions 13 and 14, consider the following parametric: 13.The initial vertical velocity is

a. 4b. 7c. 8d. -2e. -9

14.The position at t=3 is approximately how far from the initial position?a. 12b. 24c. 27d. 36e. 44

Open EndedWithout a Calculator

1. Let f ( x )=x2+7,a. find the rate of change from x=3 to x=6b. find the rate of change from x=4 to x=4.1c. find the rate of change from x to x+h

2. Given the graphs of f(x)= and g(x)= find

a. f(g(0))b. g(f(-1))c. f-1(1)d. For what value of x is g(f(x)) a maximum?

3. f ( x )=3 e2 x

a. show that f−1 (x )=12ln x3

b. graph f(x) and f-1(x)c. find f(ln 4)

Calculator Permitted4. Solve the equation x3−3 x+7=0

a. Solve x3−3 x+7≥0b. Solve x3−3 x+7<0c. How is the solution to the original equation related to the solution of the

inequalities?5. Given the function f ( x )=x3−3x+7

a. when is the function increasing? decreasing?b. when is the function at a maximum? minimum?c. How are the answers to parts a and b related?

6. 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.)

Answer Key1. G2. H3. J4. D5. E6. F7. A8. C9. B10. M11. L12. :13. Q14. N

15. P16. F17. C18. A19. M20. B21. J22. D23. H24. E25. L26. G27. K28. N

29. P30. Q31. 132. Y=x-533. Y+3=(x-2)34. X-y=535. Y-5=2(x-4)36. Y-5=-1/2(x-4)37. -1/338. A) G=9/10(t-50) +90; b) for every ten

minutes more studying, grade goes up nine points; C)85.5; D)135 minutes

39. 640. Y=6x-541. Y-4=6(x+6)42. 6x-y=543. Y-2=3(x-8)44. Y-5=-1/3(x-4)45. 446. A) y-8.55=-3/17(x-3); B)17 hours more in

training you get three minutes dropped in time; C) 8:23.235 minutes; D) 10 hrs 54,667 minutes

47. D: [-4/3, ∞) R: [13, ∞) f(0)=1548. D: reals R: [4, ∞) f(0)=649. D: x≠2; R: f(x)≠1/5 f(0)= -1/550. D: x≠1: R: f(x)≠0 f(0)=451. D: reals R=(0,∞) f(0)=1/252. Neither53. Odd54. Odd55. Even56. A) -5; B) 0; C)4; D) Domain: reals R: (-∞, -

1) U (0,∞)57. A) -2; B)-2; C) -4; D) Domain: reals R= (-

∞, -2)58. F(x)= 2x-1 x<0

3 0≤x <3-1x x≥3

59. D: (-∞, 2.5] R: [7,∞) f(0)= 7+√560. D: reals; R: [-4,∞) f(0) =-261. D: x≠ 0; R: f(x)≠2; f(0)= undefined

62. D: x≠1: R: f(x) ≠0; f(0) =263. D: 0,∞) R: reals f(0) = undefined64. Even65. Neither66. Neither67. Odd68. A) 1; B)2; C) 2; D) D:reals, R:[2,∞ ¿69. A) 4; B) 2; C) 4 D) D: reals R: [0, ∞)70. Y = -x-1 if x<-1

X+1 if -1≤x<1 2 if x ≥1

71. D: reals R: (-6,∞) Zeroes 672. D: reals R: (-∞,0) Zeros: none73. D: reals R: (-∞,6) Zeros: ln 274. D: reals R: (0, ∞) Zeros: none75. D: reals R(-1, ∞) Zeros: (ln1) (ln2)76. A) y=3ex-2 B) y= 3-2e-x C) y=3ex

77. $290.1978. 8.244 grams79. 17.329 days80. $15,83281. K= -.017; 77.069 days82. $3629.5583. $3315.9984. D: reals R: (2, ∞) zeros: none85. D: Reals R: (-2, ∞) zeros: -ln 286. D: reals R: (-∞,5) zeros: ln 2.587. D: reals R: (-∞,0) xeros: none88. D: reals R: (-2, ∞) zeros: (ln2)/ln389. A) y=-2+e-x B) y=4-e-x C) y=1+ex

90. $58.6691. 19.028 grams92. 11.553 days93. $13,12294. R=-.009589; 144.565 days after start95. $4802.6696. $10,456.5097. Y=x2; reflect over y axis, 3 left, vertical

stretch of 4, D: reals R: [6, ∞)98. Y=1/x; horizontal shrink of ½; ½ left/

vertical stretch 3; down 2; D: x≠-1/2; R: h(x) ≠-2

99. Y=√ x; reflect over y axis; 3 right; vertical stretch of 2; up 4; D: x≤3 R: [4, ∞)

100. Horizontal shrink of 3; right 2; vertical stretch of 2; down 1; D: reals; R: [-1, ∞)

101. Y=ex; reflect over y axis; horizontal shrink of ½; vertical stretch of 3; up 4; D: reals; R: (4, ∞)

102. Graph103. Graph104. Graph105. Graph106. Y= x 1/3; horizontal shrink ½; 3/2 right;

vertical stretch of 4; up 2; D: reals R: reals

107. Y= 1x2

; right 2; vertical stretch 3; up 4;

D: x≠0 ; R: (-4, ∞)

108. Y=cosx; horizointal shrink ½; π4 right;

vert stretch 2; down 3; D: reals; R: [-5, -1]109. Y=tanx; reflect over y-axis; horizontal

stretch of 2; reflect over x-axis; up 1: D: xπ2 +kn; R: reals

110. Reflect over y-axis; 2 right; up 4; D: x<2: R: Reals

111. Graph112. Graph113. Graph114. Graph115. 2 and 4116. 3√9

117.0∧75

118. 1> y>−5119. 8 and -2120. X<1 or x>7121. 1.105 or 4.307122. x≤0 or x≥ 1.854123. 133.3 feet by 100.00 feet124. 10 feet by 20 feet

125. 52.514 m3

126. 11.909”127. 10 and -2128. √10129. 0 and +/-√2130. 4>y>-1131. -8 and 0132. X<-6 or x>9133. None134. -.820 and 3.524135. 100’ by 150’136. 70 feet137. 82.981 m3

138. 18.098’

139. F-1(x) = x+23

140. F-1(x) = +/- √ x2141. F-1(x) = +/- √(1−x)3

142. F-1(x) = 3√ 14−x

143. F-1(x) = ex-4

144. F-1(x) =ln x+23

145. F-1(x) =1/4 ex+6

146. F-1(x) = x−25

147. F-1(x) = +/- √3 x+182

148. F-1(x)= (x/9)e/2

149. F-1(x) = +/- √ −3x−5

150. F-1(x)= e(x-1/2)

151. F-1(x) = e x+9

152. F-1(x) = 3e X+8

153. -1/2

154.−√24

155. −¿2

156. √33

157. -1158. -1

159.−2√103

160.512

161.−√53

162.−√414

163. Ampl: 2; Period: π ; phase shift−π3 ;

vert shift: 1

164. Ampl: 3; Period: π2 ; phase shift:

π4;vert shift :−2

165. Ampl: 1; Period: 3π; phase shift: π6 ; vert

shift: 3

166. Ampl: 1; Period: 2π3 ; phase shift:

2π3;

vert shift: -1

167. Ampl: 2/3; period π2 ; phase shift:

π2 ;

vert shift: 2168. 12/3

169.5√6161

170.3√77

171.−7√218218

172. √8511

173. ½

174. √23

175. -2

176.2√33

177. 1

178. 1179. -7/24

180.−7√28

181. 2√2182. ¾

183. Ampl: 4; Period: 4π; phase shift: π3 ; vert

shift: 2

184. Ampl: 2; Period: π2 ; Phase shift:

3π4 ;

vert shift: -3

185. Ampl: 2; Period: 8π; phase shift: −π2 ;

vert shift: 1

186. Ampl: 1; period: π3 ; phase shift:

π3 ; vert

shift: -1

187. Ampl: 3/2; period: π; phase shift: 3π2 ;

vert shift: -2188. 5/13

189.5√7474

190. √1515

191.−5√194194

192.2√1011

193. a) x(t)=20t y(t)=-16t2+30t+5 b)1.441 & .434 sec c)1.69sec d)33.8ft

194. 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 sec195. x(t)=25t y(t)=-16t2 + 40t + 4 b).5 & 2 sec c) 1.5 sec d) 37.5’

196. 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

MULTIPLE CHOICE:1. E2. C3. D4. D5. E6. D7. D8. B9. D10. D11. C12. C13. C14. C

OPEN ENDED1. A) 9; B) 8.1 C) 2x+h2. A) -1 B) 0 C) 48 D) -3 or -1/23. A) x=3e24, x/3 = e2y, ln x/3 = 2y,

½ ln (x/3) =y C) 484. A) -2.426 B) x≥ -2.426 C) the

solution to the equation is the endpoints for the inequalities

5. A) inc: (-∞, -1) U (1,∞) Dec: (-1,1) B) x=-1 x=1 C) increasing then decreasing max; Decreasing then increasing min

6. A) x (t )30 t+2 y (t )=−16 t2+20 t+4

B) 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