Which transformation was not performed on y=cos x to obtain $y=-4 \cos \left(2 x+\frac{\pi}{3}\right) ?$
A) Vertical stretch by a factor of 4
B) Reflection through the x -axis
C) Horizontal stretch by a factor of 2
D) Horizontal shrink by a factor of $\frac{1}{2}$
E) Horizontal shift left $\frac{\pi}{6}$ units

Question

Which transformation was not performed on  y=cos x  to obtain $y=-4 \cos \left(2 x+\frac{\pi}{3}\right) ?$
A) Vertical stretch by a factor of 4
B) Reflection through the  x -axis
C) Horizontal stretch by a factor of 2
D) Horizontal shrink by a factor of $\frac{1}{2}$ 
E) Horizontal shift left  $\frac{\pi}{6}$  units

Quizplus · Accepted Answer

The transformation performed includes a vertical stretch by a factor of 4 (A), a reflection through the x-axis due to the negative sign (B), a horizontal shrink by a factor of 1/2 because the coefficient of x inside the cosine function is 2, which compresses the graph horizontally (D), and a horizontal shift to the left by $\pi/6$ units, as can be deduced from the phase shift formula $y = \cos(B(x - C))$, where $C/B = \pi/3 / 2 = \pi/6$ (E). A horizontal stretch by a factor of 2 (C) is not performed; instead, the transformation involves a horizontal shrink.

Which Transformation Was Not Performed on Y=cos X y=−4cos⁡(2x+π3)?y=-4 \cos \left(2 x+\frac{\pi}{3}\right) ?y=−4cos(2x+3π​)?

Which Transformation Was Not Performed on Y=cos X $y=-4 \cos \left(2 x+\frac{\pi}{3}\right) ?$