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:
- Vertical Stretching: Multiplying cot(x) by 6 stretches the graph vertically by a factor of 6, making the amplitude of the graph larger.
- 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.
- Phase Shift: Subtracting π/2 from x inside the cotangent function shifts the graph to the right by π/2 units.
- Vertical Shift: Adding 4 to the entire function shifts the graph upward by 4 units on the y-axis.