Graph y=4cot(x)

Problem

y=4*cot(x)

Solution

1. Identify the parent function and its properties. The function y=cot(x) has a period of π vertical asymptotes at x=n*π for any integer n and xintercepts at x=π/2+n*π

2. Determine the vertical stretch. The coefficient 4 in y=4*cot(x) represents a vertical stretch by a factor of 4 This means the yvalues of the parent function are multiplied by 4

3. Locate the asymptotes. Since there is no horizontal shift or change in period, the vertical asymptotes remain at x=0 x=π x=2*π and so on.

4. Find key points for one period (0,π) The xintercept remains at (π/2,0) because 4⋅0=0 At x=π/4 y=4*cot(π/4)=4*(1)=4 At x=(3*π)/4 y=4*cot((3*π)/4)=4*(−1)=−4

5. Sketch the curve. Draw the decreasing cotangent curves between the vertical asymptotes, passing through the points (π/4,4) (π/2,0) and ((3*π)/4,−4)

Final Answer

y=4*cot(x)

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