Find the Range y=2+cot(x)

Problem

y=2+cot(x)

Solution

1. Identify the parent function, which is ƒ(x)=cot(x)

2. Recall the range of the cotangent function. The function cot(x) takes on all real values as x varies within its domain.

3. Determine the range of cot(x) in interval notation.

Range of *cot(x)=(−∞,∞)

4. Apply the vertical shift. The expression y=2+cot(x) represents a vertical shift of the parent function upward by 2 units.

5. Analyze the effect of the shift on the range. Adding a constant to a function that already spans all real numbers does not change the span.

(−∞+2,∞+2)=(−∞,∞)

Final Answer

Range of *y=2+cot(x)=(−∞,∞)

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