Use what you have learned about transformations of $y = \text{sin}\left(x\right)$ to complete parts (a) through (c).   

1. Describe what the graph of $y = 3\text{sin}( \frac { 1 } { 2 } x )$ looks like compared to the graph of $y = \text{sin}\left(x\right)$.

   Hint (a):

   Is there a horizontal or vertical shift? Does the amplitude or period change?

   Answer (a):

   Amplitude $3$, period $4π$

2. Sketch both graphs on the same set of axes.

   Hint (b):

   Since there is no horizontal or vertical shift, both graphs start at $\left(0,0\right)$.

3. Explain the similarities and differences between the two graphs.

   Hint (c):

   See parts (a) and (b).

   Use the eTool below to help answer the parts of the problem.
   Click the link at right for the full version of the eTool: INT3 9-122 HW eTool.