Which description matches the transformations y=cosx undergoes to produce y= -2cos3x

a. horizontal compression by factor 1/3, vertical stretch by factor 2, then a reflection through the x-axis
b. reflection through the y-axis, vertical shift of 2 units, horizontal shift right by 3 units
c. horizontal shift 2 units, then vertical shift up by 3 units
d. horizontal stretch by factor 2, reflection through the x-axis, then the vertical stretch by factor 3

 A. Horizontal compression by factor 1/3, vertical stretch by factor 2, then a reflection through the x-axis

Step-by-step explanation:

Since, If there is a function, y= a cos bx

Then a shows vertical stretch while b shows horizontal compression.

Here, Given function, y= cos x

After transformation, It is giving y = -2 cos 3x

therefore here is a horizontal compression occurs with factor 1/3.

Also Negative sign shows there also did reflection through x-axis.

And, It also, stretched vertically by factor 2. ( also shown in the below graph)

Thus, Option A) is correct.      

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