Math Grade 11, sinusoidal functions

Please go to the above link and you will find the graph, and answer the following two questions. 

  • Which transformations applied to the graph of y = sin(x) would result in the graph shown above?
  • Write the equation of the graph.
  • please show each transformation clearly in steps. thanks.

    Expert Answers

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    We see that the sine graph has an amplitude of 2, and is reflected vertically through the x-axis.  This is because it is going down at the origin instead of going up like a regular sine graph.  Also, the graph has not been shifted away from the origin, since there is a point of symmetry that goes through (0,0).  Finally, the graph goes through one and a half complete cycles in 180 degrees.  Since `k=360/T` and `T={3 cdot 180}/2=270` is the period, then we see that `k=360/270=4/3` is the horizontal compression.

    The three transformations (vertical stretch of 2, vertical reflection, horizontal compression 4/3) is combined into `y=-2sin({4x}/3)` .

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