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To map A into B:
Scale the graph by a factor of 0.5 along the x-axis direction(graph becomes more 'fat'), followed by a factor of 2 along the y-axis direction(graph becomes 'taller'). And a translation of 2 units in negative x direction, and translation of 2 units in the positive y direction.
Scale the graph by a factor of 0.5 along the x-axis direction(graph becomes more 'fat'), followed by a factor of 2 along the y-axis direction(graph becomes 'taller'). And a translation of 2 units in negative x direction, and translation of 2 units in the positive y direction.