You will explore graphically the general sine function

as you change the values of the constants A, B, C, and D. Use a CAS or computer grapher to perform the steps in the exercises.

Set the constants A = 3, B = 6, D = 0.

a. Plot ƒ(x) for the values C = 0, 1, and 2 over the interval -4π ≤ x ≤ 4π. Describe what happens to the graph of the general sine function as C increases through positive values.

b. What happens to the graph for negative values of C?

c. What smallest positive value should be assigned to C so the graph exhibits no horizontal shift? Confirm your answer with a plot.

f(x) = A sin x c ) + 2TT -(x B C) + D