Graph 0.5tan(x)

Problem

y=0.5*tan(x)

Solution

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

2. Determine the vertical stretch or compression. The coefficient 0.5 indicates a vertical compression by a factor of 0.5 This means the yvalues of the parent function are halved.

3. Locate key points within one period (−π/2,π/2) The center point is (0,0) In the parent function, the points at x=−π/4 and x=π/4 are (−π/4,−1) and (π/4,1) For this function, they become (−π/4,−0.5) and (π/4,0.5)

4. Identify the asymptotes. Since there is no horizontal shift or period change, the vertical asymptotes remain at x=−π/2 and x=π/2

5. Sketch the curve by drawing a smooth, increasing curve that passes through (−π/4,−0.5) (0,0) and (π/4,0.5) approaching the vertical asymptotes on either side. Repeat this pattern every π units.

Final Answer

y=0.5*tan(x)

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