Question

To produce the graph of the function y =0.5cot(0.5x), what transformations should be applied to the graph of the parent function Y = cot(x)? a horizontal compression to produce a period of and a vertical compression

A.a horizontal compression to produce a period of î and a vertical stretch
B.a horizontal stretch to produce a period of 27 and a vertical compression
C.a horizontal stretch to produce a period of 2x and a vertical stretch"

Answer 1

To obtain the graph of y = 0.5cot(0.5x) from y = cot(x), apply a horizontal stretch to achieve a period of 2π and a vertical compression by a factor of 0.5.

Step-by-step explanation:

To transform the graph of the parent function y = cot(x), which has a period of π, into the graph of the function y = 0.5cot(0.5x), we must apply two transformations.

1. First, a horizontal stretch is applied by a factor of 2, because the coefficient of x inside the cotangent function is 0.5, which is the reciprocal of 2. This stretches the graph so that it has a new period of 2π, since the period of the cotangent function is π divided by the absolute value of the coefficient of x.
2. Second, a vertical compression by a factor of 2 occurs because of the coefficient 0.5 applied to the cotangent function. This scales down the y-values by a factor of 2.

In summary, to produce the graph of y = 0.5cot(0.5x), a horizontal stretch to produce a period of 2π and a vertical compression by a factor of 0.5 (or 1/2) are necessary.