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by: Marquise Graham


Marquise Graham
GPA 3.8


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Class Notes
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This 11 page Class Notes was uploaded by Marquise Graham on Saturday September 19, 2015. The Class Notes belongs to MAC 1105 at University of Florida taught by Staff in Fall. Since its upload, it has received 31 views. For similar materials see /class/207049/mac-1105-university-of-florida in Calculus and Pre Calculus at University of Florida.




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Date Created: 09/19/15
L14 Graphing Techniques Transformations Mathematical Models Transformations Vertical and Horizontal Translations c gt 0 To c c C 6 6 Example Graph the function yx7371 Vertical Compressions and Stretches l MLth a e5 4 3 2f 1 2 3 4 5 Is E o l 39 39 39 l I I l I 39I 2 Example Above is the graph of y 2 xi In the same plane graph y 2x and y x The graph of y a f x a i O is obtained from the graph of y f x by multiplying by a the y coordinate of each point that is on the graph of f Compared to the graph of y f x the graph of y a f x is stretched vertically if lal gt1 compressed vertically if 0 lt al lt l 132 Horizontal Compressions and Stretches 123447372 1234 2 3 A 5 s 77 ix 9 fltxgtx3 fZx2x3 fend The graph of y fwc a i 0 is obtained from the graph of y f x by multiplying by l the x a coordinate of each point Which is on the graph off Compared to the graph of y f x the graph of y f wc is stretched horizontally if 0 lt lal lt l compressed horizontally if Ial gt 1 Re ections across the xAxis and yAXis In order to obtain the graph of y f x re ect the graph of y f x across the xaxis In order to obtain the graph of y f x re ect the graph of y f x across the yaxis Example Graph the functions y x 1 y l x Build and Analyze Functions mm 1 Make a sketch or a chart 2 Find relation between the variables 7 build the function 3 Analyze the function Example Let P xy be a point on the graph of y 2x 5 Build and analyze the function d d x that expresses the distance from the point P to the origin in terms of the xcoordinate of the point P Answer the questions What is d when x 0 What is d when x 2 Use a graphing utility to graph the function d dx Find the minimum value of d rounded to 3 decimal places Give the value of x for which d is a minimum Give the point on the graph y 2x 5 which is closest to the origin Example Geometry A rectangle is inscribed in an upper half of a circle of radius 3 with center at the origin Two comers of the rectangle lie on the xaXis Two other corners are on the graph of the semicircle Let P xy be the comer of which lies in quadrant I Write the area A of the rectangle as a function of x and determine the domain of the function Use a graphing utility to graph A Ax For what value of x is A the maximum Round your answer to two decimal places Give the maximum value of A 138 Variation A quantity y varies directly with quantity x or y is directly proportional to x if there is a nonzero constant k such that y kx A quantity y varies inversely with quantity x or y is inversely proportional to x if there is a nonzero constant k such that k y x The number k is called the constant of proportionality When a quantity Q is proportional to the product of two or more quantities we say that Q varies jointly with these quantities The combination of direct and0r inverse variation is called combined variation 139 Physics Hooke s Law The force f x in newtons required to maintain a spring stretched x m beyond its natural length is directly proportional to x Provided that x is not too large A force of 40 N is required to hold a spring that has been stretched from its natural length of 10 cm to a length of 15 cm Find the force that is required to stretch the spring 8 cm beyond its natural length 140 L14 1 Which ofthe following statements isare true A The graph offx ITt is the re ection ofthe graph of gx J across the xaxis B The graph offx are and gx 4 are identical c The graph of fx J37 t is obtained from the graph of gx J by first re ecting gx across the yaxis and then shifting right 3 units D The graph of y it is obtained from the graph of y 8 by either compressing vertically by afactor of4 or stretching horizontally by afactor of 2 2 Find the function that is finally er ollowing re ected across the xaxis 3 Use the graph of x2 to write the formula for the function gx Fir 2 7 HM 4 1fthe force acting on an object tatheameLL Icui rr mass1fan object with amass of54 kilograms accelerates at arate of4 meters per second per second msecz by aforce find the acceleration ofan object with mass of6 kilograms that is pulled by the same force


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