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