Modeling with Trigonometric Expressions and Functions: Part Two — Test

Question 11 • Precalculus

Which transformation should be applied to the graph of the function y is equal to cotangent of x to obtain the graph of the function y is equal to 6 cotangent open paren 3 x minus pi over 2 close paren plus 4 ?

Answer

a vertical stretch, a horizontal compression to make the period pi over 3 , a horizontal shift of pi over 2 units to the right, and a vertical shift of 4 units up

a vertical stretch, a horizontal compression to make the period 2 pi over 3 , a horizontal shift of pi over 2 units to the right, and a vertical shift of 4 units up

a vertical stretch, a horizontal compression to make the period 2 pi over 3 , a horizontal shift of pi over 6 units to the right, and a vertical shift of 4 units up

a vertical stretch, a horizontal compression to make the period pi over 3 , a horizontal shift of pi over 6 units to the right, and a vertical shift of 4 units up

Explanation

Factor the expression inside cotangent: 3x − π/2 = 3(x − π/6), so the graph shifts π/6 units to the right. The factor 3 makes the period π/3 (the cotangent period π divided by 3), while the outside factor 6 stretches the graph vertically and +4 shifts it up 4 units. This matches choice D.

AI-written and checked against the verified answer.

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