combined_transformations

# combined_transformations - Combined transformations of...

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Combined transformations of graphs Example 1 : Sketch the graph of = y - + x 2. Solution : Reflecting the graph of = y x in the x axis gives the graph of = y - x ( green graph ). Shifting the graph of = y - x upwards through 2 units gives the graph of = y - + x 2 ( red graph ). Example 2 : Sketch the graph of = y - - x 2 4. Solution : Reflecting the graph of = y x 2 (dotted graph) in the x axis gives the graph of = y - x 2 ( green graph ). Shifting the graph of = y - x 2 downwards through 4 units gives the graph of = y - - x 2 4 ( red graph ). Alternatively, the graph of = y x 2 can be shifted upwards to give the graph of = y + x 2 4 ( purple graph ) and then this graph can be reflected in the x axis to give the graph of = y - ( ) + x 2 4 , which is equivalent to = y - - x 2 4.

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Example 3 : Sketch the graph of = y + 3 - x 2 1 . Solution : The graph of = y 3 x can be obtained by stretching the graph of = y x with a factor of 3 parallel to the y axis. The graph of = y + 3 - x 2 1 can be obtained by shifting the graph of = y 3 x horizontally through 2 units to the right and one unit vertically upwards. Example 4 : Sketch the graph of = y - 3 x 5. Solution : The graph of = y 3 x ( blue graph) can be obtained by scaling the y coordinates on the graph of = y x (dotted graph) with the factor 3 so that the graph stretches parallel to the y axis. Then the graph of ( red graph) can be obtained by shifting the graph of = y 3 x through 5 units downwards. The x intercept occurs where = - 3 x 5 0, that is, where = 3 x 5, which is equivalent to = x 5 3 , giving = x 25 9 = 2 7 9 ~ 2.7778.
Example 5 : Sketch the graph of = y - - x 3 4. Solution : The graph of = y - x 3 ( blue graph) can be obtained by shifting the graph of = y x (dotted graph) to the right 3 units. Then the graph of

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## This note was uploaded on 11/12/2011 for the course MATH 111 taught by Professor Uri during the Spring '08 term at Rutgers.

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combined_transformations - Combined transformations of...

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