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Vertical ShiftsClass WorkPart 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.3543300753745342900753745 3429001536701. a) 2. a) 3543300100330 b) b) Part 2: 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) draw the graph of both on one graph.i) y=x2ii) Move down 2iii)i) y=1xii) Move up 3iii)i) y=xii) Move up 1iii)i) y=xii) Move down 1iii)i) y=exii) Move down 4iii)Vertical ShiftsHomeworkPart 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.3543300868045342900868045 8. a) 9. a) 35433006413534290064135 b) b) Part 2: 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) draw the graph of both on one graph.i) y=xii) Move up 3iii)i) y=1xii) Move down 2iii)i) y=cos?(x)ii) Move up 2iii)i) y=xii) Move up 3iii)i) y=log?(x)ii) Move down 4iii)Spiral Review15. (2x + 3)(x – 1)16. -y34x2 17. x3 – 3x2 +5x – 318. 4x2 + 12x + 9Horizontal ShiftsClass WorkPart 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.3543300753745342900753745 19. a) 20. a) 3543300100330342900100330 b) b) Part 2: 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) draw the graph of both on one graph.i) y=x2ii) Move right 2iii) i) y= 1xii) Move left 3iii) i) y=xii) Move left 1iii)i) y=xii) Move right 1iii)i) y=exii) Move right 4iii)Horizontal ShiftsHomeworkPart 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.3543300868045342900868045 26. a) 27. a) 35433006413534290064135 b) b) Part 2: 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) draw the graph of both on one graph.28. i) y= x3ii) Move right 3iii)i) y=1xii) Move right 2iii)i) y=xii) Move left 4iii) i) y=xii) Move right 5iii)i) y=log?(x)ii) Move right 2iii)Spiral Review33. x3 – 3x2 + 3x +134. (2x – 5)(3x – 2)35. ac6b4 36. x2 ReflectionsClass WorkPart 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.3543300753745342900753745 37. a) 38. a) 3543300100330342900100330 b) b) Part 2: 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) draw the graph of both on one graph.i) y=x2ii) Reflect over x-axisiii)i) y=1xii) Reflect over y-axisiii)i) y=xii) Reflect over y-axisiii)i) y=xii) Reflect over x-axisiii) i) y=exii) Reflect over y-axisiii)ReflectionsHomeworkPart 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated. 35433003175342900317544. a) 45. a) 35433001016034290010160 b) b) Part 2: 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) draw the graph of both on one graph.i) y= x2ii) Reflect over y-axisiii)i) y=x3ii) Reflect over x-axisiii)i) y=cos?(x)ii) Reflect over x-axisiii)i) y=1xii) Reflect over x-axisiii)i) y=log?(x)ii) Reflect over x-axisiii)Spiral Review51. 5652. 8x3 +12x2 + 6x + 153. 3x3 +11x2 – 454. 3x7z5y5 Vertical Stretches and ShrinksClass WorkPart 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.3543300753745342900753745 55. a) 56. a) 3429001003303543300100330 b) b) Part 2: 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) draw the graph of both on one graph.i) y=x2ii) Vertical stretch of 2iii)i) y=1xii) Vertical stretch of 3iii)i) y=xii) Vertical shrink of 12iii)i) y=xii) Vertical shrink of 23iii)i) y=exii) Vertical stretch of 3iii)Vertical Stretches and ShrinksHomeworkPart 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.3086100982345342900868045 62. a) 63. a) 30861006413534290064135 b) b) Part 2: 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) draw the graph of both on one graph.i) y=x3ii) Vertical stretch of 4iii)i) y=1xii) Vertical shrink of 0.25iii)i) y=cos?(x)ii) Vertical shrink of 12iii)i) y=xii) Vertical stretch of 3iii)i) y=log?(x)ii) Vertical shrink of 13iii)Spiral Review69. x270. -3771. 27x3 + 54x2 +36x + 872. -2xzy5 Horizontal Stretches and ShrinksClass WorkPart 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.3543300753745342900753745 73. a) 74. a) 354330010033034290032385 b) b) Part 2: 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) draw the graph of both on one graph.i) y=x2ii) Horizontal shrink of 2iii)i) y=1xii) Horizontal shrink of 3iii)i) y=xii) Horizontal stretch of 12iii)i) y=xii) Horizontal stretch of 23iii)i) y= exii) Horizontal shrink of 3iii)Horizontal Stretches and ShrinksHomeworkPart 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.3543300982345342900982345 80. a) 81. a) 354330010985534290042545 b) b) Part 2: 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) draw the graph of both on one graph.i) y=x3ii) Horizontal shrink of 4iii)i) y=1xii) Horizontal stretch of .25iii)i) y=x2ii) Horizontal stretch of 14iii)i) y=xii) Horizontal shrink of 2iii)i) y=log?(x)ii) Horizontal stretch of 12iii) Spiral Review87. x2 + 10x +2588. (3x + 5)(3x – 5)89. Unfactorable90. -12x7 – 15x5 Combining TransformationsClass WorkPart 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.3543300807085342900807085 91. a) 92. a) 35433003937034290039370 b) b) Part 2: 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) draw the graph of both on one graph.i) y=x2ii) Reflect over y-axis, move right 3, vertical stretch of 4, move up 6iii)i) y=1xii) Horizontal shrink of 2, move left 1, vertical stretch of 3, move down 2iii)i) y=xii) Reflect over y-axis, move right 3,vertical stretch of 2, move up 4iii)i) y=xii) Horizontal shrink of 3, move right 2, vertical stretch of 2, move down 1iii)i) y=exii) Horizontal shrink of 2, reflect over y-axis, vertical stretch of 3, move up 4iii)Combining TransformationsHomeworkPart 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.3543300868045342900868045 98. a) 99. a) 35433004953034290049530 b) b) Part 2: 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) draw the graph of both on one graph.i) y=x3ii) Horizontal shrink of 2, move right 3, vertical stretch of 4, move up 2iii)i) y=1xii) Move right 2, vertical stretch of 3, move down 4iii)i) y=xii) Horizontal stretch of 13, move right 6, reflect over x-axisiii)i) y=xii) Reflect over y-axis, move down 3iii)i) y=log?(x)ii) Reflect over y-axis, move right 2, move up 4iii)Spiral Review105. 9x2 – 24x + 16106. 3m-5n2 107. (5x + 1)(5x – 1) 108. Unfactorable Operations with FunctionsClass Work109. a) hx=3x2+3x-2-5 limx→-∞∞ limx→∞∞b) 11c) -3d) 15110. a) hx=(3x2-4)(3x-2-1)limx→-∞∞ limx→∞∞b) 24c) -4d) 56111. a) hx=3x2-43x-2-1 limx→-∞∞ limx→∞∞b) 223c) -4d) 117a) hx=6x2-33x-2-5 limx→-∞∞ limx→∞∞b) 7c) -11d) -5a) hx=3x2-4(3x-2-1)2 limx→-∞13 limx→∞13b) 89c) -4d) 849Spiral Review114. 115. 116. (4x + 9)(4x – 9)117. 8x3 + 12x2 + 4x + 6 Operations with FunctionsHomeworka) hx=x+5-(2x+1)2limx→-∞-∞ limx→∞-∞b) -6.55c) 1d) -78a) hx=xx+5 limx→-∞0 limx→∞∞b) 2.45c) -2d) 12a) hx=(2x+1)2x+5limx→-∞∞ limx→∞∞b) 3.67c) 12d) 27a) hx=5(2x+1)2-2x+5 limx→-∞∞ limx→∞∞b) 40.1c) 1d) 399a) hx=-x+5(2x+1)4limx→-∞0 limx→∞0b) -.03c) -2d) -12187Spiral Review123. y=2(x-2)2+2124. y=-3x+2+3125. y=-2x+1 Composite FunctionsClass Worka) fgx=-6x+10b) -2a) fgx=25x2-10x+2b) 82a) fgx=22x2-11b) -23a) fgx=x+2x+1b) 23a) fgx=x-13b) 1Spiral Review131.132. 133. -x105y134. 16m7n7 Composite FunctionsHomeworka) fgx=2x+2b) 6a) fgx=8x2+24x+13b) 93a) fgx=-13x2-8b) -14a) fgx=2-x-x+6+3b) 3a) fgx=x-12-4b) -3Spiral Review140. y=x+2-2141. y=-(x-2)3+1142. -4a6b9Inverse FunctionsClass Worki) f1x=x+23ii) iii) D: all reals R: all reals limx→-∞∞ limx→-∞∞i) f1x=±x-12ii) iii) D: x≥1 R: all reals limx→∞undefined limx→∞±∞i) f1x=±-x3+1ii) iii) D: x≤1 R: all real numbers limx→-8±∞ limx→∞undefinedi) f1x=3+2x4xii) iii) D: x≠0 R: y≠12 limx→-∞12 limx→∞12i) f1x=10x-2ii) iii) D: all reals R: y≥-2 limx→-∞-2 limx→∞∞Spiral Review148. f°gx=x4+2x+1149. (4x – 5y)(4x + 5y)150. 16x12y8151. H. shrink 3, reflect y, ↑ 2 Inverse FunctionsHomeworki) f1x=x-25ii) iii) D: all reals R: all reals limx→-∞-∞ limx→∞∞i) f1x=±32x+9ii) iii) D: x≥-6 R: all reals limx→-∞undefined limx→∞±∞i) f1x=±x4+4ii) iii) D: all reals R: -2≥y≤2 limx→-∞±∞ limx→∞±∞i) f1x=5x-23xii) iii) D: x≠0 R: y≠53 limx→-∞53 limx→∞53i) f1x=ex+2ii) iii) D: all reals R: y>2 limx→-∞2 limx→∞∞Spiral Review157. x4-4x3+6x2-4x+1158. (8x – 1)(2x + 3)159. -27x6y12160. ← 2, v. stretch 2, reflect x, ↓ 5 Piecewise FunctionsClass Work161. a. f(-2) = 465b. f(1) = 8c. f(4) = 74d. D: all reals R: y≥-2e. 162. a. f(-2) = -10b. f(0) = 2c. f(4) = 4d. D: all reals R: 2≥y<3e. 163. a. f(-5) = -1b. f(0) = -4c. f(4) = 6d. D: all reals R: y<5e. 164. b = -3Piecewise FunctionsHomework165. a. f(-2) = -2b. f(0) = 6c. f(3) = -3d. D: all reals R: y<6e. 166. a. f(-2) = -83b. f(0) = 0c. f(4) = -643d. D: all reals R: all realse. 167. a. f(-5) = -2b. f(0) = -4c. f(4) = 1d. D: all reals R: y<1e. 168. a = -1.2 b = -3.6Spiral Review169. 3x2-1170. (9x + 4y)(9x – 4y)171. -8x7y6172. → 2, reflect x, ↓ 5 Unit Review QuestionsMultiple ChoiceDescribe the transformation of the parent function f(x) = x2 to g(x) = x2 – 1shift left 1shift right 1shift down 1shift up 1Describe the transformation of the parent function f(x) = |x| to g(x) = | x+1|shift left 1shift right 1shift down 1shift up 1Describe the transformation of the parent function f(x)= [x] to g(x)= [2x]horizontal stretch of scale factor 2horizontal stretch of scale factor 1/2vertical stretch of scale factor 2vertical stretch of scale factor 1/2Describe the transformation of the parent function f(x)= 1x to g(x)= 2xhorizontal stretch of scale factor 2horizontal stretch of scale factor 1/2vertical stretch of scale factor 2vertical stretch of scale factor ?Describe the transformation of the parent function f(x)= log(x) to g(x)= log(-x)horizontal reflectionvertical reflectiondoes not affect f(x) since it is symmetricalnot possible because log(x) is undefined for negativesThe order of the following transformation of hx=x to hx=43-x+5 isSlide 3 right, stretch 4 vertically, slide 5 upSlide 3 left, stretch 4 vertically, slide 5 upReflect over the y-axis, slide 3 right, stretch 4 vertically, slide 5 upReflect over the y-axis, slide 3 left, stretch 4 vertically, slide 5 upfx=3x2-2 , gx=4-x, and hx=fx-gx. h(3) =78262418fx=3x2-2 , gx=4-2x, and hx=fx/gx. h(3) =-50-2525-12.5fx=(3x)2-4 , gx=5-4x, and hx=fxgx. h(3) =-539-38.5-77fx=3x2-2 , gx=4-x, and hx=f(gx). h(3) =-5-3-11fx=3x2-2 , gx=4-x, and hx=g(f(x)). h(2a+1) =-12a2-12a+325-36a+12a2-6a2+512a2+3Given fx=2x3-2, find f-18-102235122Given fx=2x3-2 and f-1a=-3, find a.-27-33-56undefinedax=2x-1 if x≤3-4x+2 if x>3 , find a(3).5-105 or -10Undefinedbx=3x+2a if x<24a-x if x≥2, find a such that b(x) is continuous-8-448Unit Review Questions354012515875Extended ResponseGiven the function of f(x) as shown at the right hx=2x2+xm if x≤3xm2 if x>3m=3,-2For which value of m is the rate of change about h(3) the closest?Find h(3) in terms of m.Given hx=x-2x2-4 and gx= x+3x2+5x+6, describe the type and locations of any discontinuities of f(x)Vertical Asymptote at x=-2.5, Horizontal Asymptote at y=0Vertical Asymptote at x=0, Horizontal Asymptote at y=1Vertical Asymptote at x=-2, Horizontal Asymptote at y=0Write a piecewise function f(x) so that the hole in g(x) is removed.People enter a park at a rate of Et=8t if t≤62t if t>6 where t is the number of hours after opening. People leave the park at a rate of Lt=4t if t≤63t+c if t>6. The park is open 12 hours a day. Write an, P(t) equation for the rate of change in the number of people in the park in terms of E(t) and L(t).Create the piecewise function for P(t).Find c so that there is no one in the park at closing.Does the answer in part c make sense? Explain. ................
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