Consider the function y = 4 sin ( 2x /3 ) for x . Follow the steps below to sketch the graph of y. (a) State the amplitude and period in the graph of...

Consider the function y = 4 sin ( 2x − π/3 ) for −π ≤ x ≤ π. Follow the steps below to sketch the graph of y.

(a) State the amplitude and period in the graph of this function.

(b) Solve y = 4 sin ( 2x − π/3 ) for −π ≤ x ≤ π to find the horizontal intercepts (x-intercepts) of the function.

(c) Find the values of x for −π ≤ x ≤ π for which the maximum and the minimum values of the function occur.

(d) State the range of the function.

(e) Using the information obtained in (a)-(d), draw the graph of y = 4 sin ( 2x − π/3 ) for −π ≤ x ≤ π