which description matches the transformations y=cos x undergoes to produce y=-2cos3x?A. horizontal compression by factor 3, vertical stretch by factor 2, then reflection across the x-axis.B. horizontal shift left 2 units, then vertical shift up by 3 units.C. reflection across the y-axis, vertical shift up by 2 units, horizontal shift right by 3 units.D. horizontal stretch by factor 2, reflection across the x-axis, then vertical stretch by factor 3.

Answer:horizontal compression by factor 3, vertical stretch by factor 2, then reflection across the x-axis ⇒ answer AStep-by-step explanation:* Lets revise some transformation- A vertical stretching is the stretching of the graph away from  the x-axis# If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched   by multiplying each of its y-coordinates by k.# If k should be negative, the vertical stretch is followed by a reflection   across the x-axis.  - A horizontal compression is the squeezing of the graph toward  the y-axis.# If k > 1, the graph of y = f(k•x) is the graph of f(x) horizontally   compressed by dividing each of its x-coordinates by k.* Lets solve the problem∵ y = cos x∵ y = -2 cos 3x- At first cos x multiplied by -2∵ y multiplied by -2∵ 2 > 1 ∴ y = cos x is stretched vertically by factor 2∵ The factor 2 is negative∴ y = cos x reflected across the x-axis∴ The function y = cos x stretched vertically with factor 2 and then   reflected across the x-axis ⇒ (1)∵ cos x changed to cos 3x∵ x multiplied by 3 ∵ 3 > 1∴ y = cos x compressed horizontally by factor 3∴ The function y = cos x compressed horizontally by factor 3 ⇒ (2)- From (1) and (2) * The function y = cos x has horizontal compression by factor 3,   vertical stretch by factor 2, then reflection across the x-axis to   produce y = -2 cos 3x