Algebra-2

The correct answer is B. Vertical reflection, vertical stretch by a factor of 2, horizontal compression by a factor of 3, horizontal shift to the right by , and vertical shift upwards by 3.

Let's break down the transformation of the parent function step by step:

1. Vertical reflection: The negative sign in front of the cosine function reflects the graph vertically.

2. Vertical stretch by a factor of 2: The coefficient -2 stretches the graph vertically by a factor of 2 compared to the parent function.

3. Horizontal compression by a factor of 3: The coefficient 3 in front of the variable x compresses the graph horizontally by a factor of 3 compared to the parent function.

4. Horizontal shift to the right by