Graph y=2cot(x)

Problem

y=2*cot(x)

Solution

1. Identify the parent function and its properties. The parent function is y=cot(x) which has vertical asymptotes where sin(x)=0 specifically at x=n*π for any integer n

2. Determine the period of the function. The period of cot(x) is π Since there is no horizontal stretch or compression (the coefficient of x is 1, the period remains π

3. Identify the vertical stretch. The coefficient 2 in front of the cotangent function indicates a vertical stretch by a factor of 2 This means the function will increase and decrease more steeply than the standard cotangent graph.

4. Locate key points within one period (0,π) The xintercept occurs at the midpoint of the asymptotes, which is x=π/2 At x=π/4 y=2*cot(π/4)=2*(1)=2 At x=(3*π)/4 y=2*cot((3*π)/4)=2*(−1)=−2

5. Sketch the asymptotes and the curve. Draw vertical dashed lines at x=0 x=π and x=2*π Plot the points (π/4,2) (π/2,0) and ((3*π)/4,−2) then draw the characteristic decreasing cotangent curve through them.

Final Answer

y=2*cot(x)

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