Use the GeoGebra File below to schow how a, b, c, and d affect their graphs and then answer the questions below.

Use the graph above to answer the following questions.
1) How does the a variable affect the graphs qualitatively?
2) How does the graph of y = 2 sin(x) differ from the graph of y = sin(x)?
3) How does the b variable affect the graphs qualitatively?
4) How does the graph of y = cos(4x) differ from the graph of y = cos(x)?
5) How does the c variable affect the graphs qualitatively?
6) How does the graph of y = tan(x + 2) differ from the graph of y = tan(x)?
7) How does the d variable affect the graphs qualitatively?
8) How does the graph of y = cos(x) - 4 differ from the graph of y = cos(x)?
9) If provided with the graph of y = 2 sin(3x) + 1, how would you sketch a graph y = 2 csc(3x) + 1?
10) Connect the following vocabulary to the a, b, c, or d variable that controls it.
(period, phase shift, amplitude, vertical shift)
11) How long are the periods for the following functions? (Express your answer in both radians and degrees)
y = sin(x)
y = cos(x)
y = tan(x)
12) If given the equation 3 sin(2x) - 1 = 4, how can you use the graph to conclude that there is no solution?