Graph the function from and y = 2 - 4sin²3 x A) B) C) D)

Question

Quizplus · Accepted Answer

The general form of the function y = a + bsin(cx + d) shifts the graph vertically by a units, stretches it vertically by |b| units, compresses it horizontally by factor of |c| and shifts it horizontally by d/|c| units to the left or right depending on the sign of d. Comparing this to the given equation y = 2 - 4sin(S1U1P12 S1S1P03 x), we see that a = 2, b = -4, c = 1 and d = S1S1P03. Since b is negative, the graph is reflected about the x-axis. Since c = 1, there is no compression or stretching horizontally. Therefore, we only need to determine the phase shift of the function.

To find the phase shift, we need to solve for the argument of the sine function when it is equal to zero.

S1U1P12 S1S1P03 x = 0

x = 0, S1S1P02

The phase shift is given by the difference between the two roots:

(S1S1P02) - 0 = S1S1P02

Therefore, the graph is shifted to the right by S1S1P02 units.

Combining all these transformations, we get the graph shown in choice B.

Graph the Function from and Y = 2 -