Graph y=3cot(x)

Problem

y=3*cot(x)

Solution

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

2. Determine the vertical stretch. The coefficient 3 indicates a vertical stretch by a factor of 3 This means the yvalues of the parent function are multiplied by 3

3. Locate the x-intercepts. The xintercepts occur where cot(x)=0 which are at x=π/2+n*π For the first period, the intercept is at (π/2,0)

4. Identify 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.

5. Plot key points to determine the shape. In the interval (0,π) calculate values at x=π/4 and x=(3*π)/4

y=3*cot(π/4)=3*(1)=3

y=3*cot((3*π)/4)=3*(−1)=−3

6. Sketch the graph by drawing the decreasing curves between the vertical asymptotes, passing through the points (π/4,3) (π/2,0) and ((3*π)/4,−3)

Final Answer

y=3*cot(x)

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