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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

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5 votes

Final answer:

To transform y=cot(x) into y=6 cot(3x-π/2)+4, apply a vertical stretch by a factor of 6, a horizontal compression by 1/3, a phase shift right by π/2, and a vertical shift upward by 4 units.

Step-by-step explanation:

To obtain the graph of the function y=6 cot(3x-π/2)+4 from the graph of the function y=cot(x), you should apply a series of transformations. These transformations include a vertical stretching by a factor of 6, a horizontal compression by a factor of 1/3, a phase shift (or horizontal shift) to the right by π/2, and finally, a vertical shift upward by 4 units.

Here is the step-by-step explanation:

  1. Vertical Stretching: Multiplying cot(x) by 6 stretches the graph vertically by a factor of 6, making the amplitude of the graph larger.
  2. Horizontal Compression: Replacing x with 3x compresses the graph horizontally by a factor of 3, which means the period of the cotangent function becomes shorter.
  3. Phase Shift: Subtracting π/2 from x inside the cotangent function shifts the graph to the right by π/2 units.
  4. Vertical Shift: Adding 4 to the entire function shifts the graph upward by 4 units on the y-axis.

User Abstrus
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3 votes

Answer:

the answer is A.

Step-by-step explanation:

i took the test

User Bradheintz
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