Question

Which transformation should be applied to the graph of the function y=cot(x) to obtain the graph of the function y=6 cot(3x-pi/2)+4

Answer 1

option 1

Explanation:

Answer 2

The correct answer is the first one.

Explanation:

Let's analyse the effect of each modification in the function.

The value 6 multiplying the cot function means a vertical stretch.

The value of 3 multiplying the x inside the function is a horizontal compression, which causes the period to be 3 times lower the original period.

The original period of the cotangent function is pi, so the horizontal compression will make the period be pi/3.

The value of -pi/2 inside the cotangent function normally causes a horizontal shift of pi/2 to the right, but the x-values were compressed by a factor of 3 (horizontal stretch), so the horizontal shift will be 3 times lower: (pi/2) /3 = pi/6

And the value of 4 summing the whole equation is a vertical shift of 4 units up.

So the correct answer is the first one.