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a Each ofthe six functions y = fX below can be written in the standard for M y = C|A(x 8}| + D, for some
a Each ofthe six functions y = fX below can be written in the "standard for M" y = C|A(x 8}| + D, for some constants A, B, C, D. Find these constants, describe the precise order of graphical operations involved in going from the graph of y = IXI to the graph of y = fx} [paying close attention to the order}, sketch the graph, write out the multipart rule, and calculate the coordinates of the "vertex" of the graph. Describe the precise order of graphical operations. 0 vertical shift down by 4 0 horizontal shift left by4 O vertical shiFt up by 4- 0 horizontal shift right by 4 Sketch the graph. y 4 10 5 51 -10 X -5 5 10 -10 X -5 5 10 -5- O -10 O -10 10- 10/ 5 -10 -5 X 5 10 -10 X -5 5 10 -5 -51 O -10 O -10Write out the multipart rule. x 54 f( x) = 4 EX Calculate the coordinates of the "vertex" of the graph. (x, V) = (ii) f(x) = 2|x+51 A = B = C = D = Describe the precise order of graphical operations. O horizontal shift right by 5; vertical expansion by a factor of 2 horizontal shift left by 5; vertical compression by a factor of 2 O horizontal shift left by 5; vertical expansion by a factor of 2 O horizontal shift left by 2; vertical expansion by a factor of 5 Calculate the coordinates of the "vertex" of the graph. (x, V ) = (iii) f(x) = 12x - 31 A = B = C = D = Describe the precise order of graphical operations. O horizontal compression by a factor of 2; horizontal shift right by No/ W O horizontal expansion by a factor of 2; horizontal shift left by N / W O horizontal compression by a factor of 2; horizontal shift left by Now O horizontal expansion by a factor of 2; horizontal shift right by N/ wSketch the graph. 4 10 10 5 X -10 -5 5 10 -10 -5 5 10 -5 -5 -10 -10 O O 10 10/ 5 X -10 -5 5 10 -10 -5 5 10 -5 -5 -10 - 10 O Write out the multipart rule. f ( x ) = . ExCalculate the coordinates of the "vertex" of the graph. w=r-> Describe the preciSe order of graphical operationS. D horizontal comprESSion by a factor of 2; horizontal Shift left by 3 '3 horizontal expanSion by a factor of 2; horizontal Shift right by 3 '3 horizontal expanSion by a factor of 2; horizontal Shift left by 3 '3 horizontal compreSSion by a factor of 2; horizontal Shift right by 3 Sketch the graph. 4 - 4 10- 10 -10 -5 X 5 10 -10 LX -5 5 10 -5 -5 O -10 O -10 10 10/ 15/ -10 -5 5 10 10 L X -5 5 10 -51 -5 O -10 O -10 Write out the multipart rule. x
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