Graph y=-2tan(x)

Problem

y=−2*tan(x)

Solution

1. Identify the parent function and its properties. The base function is 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 transformations applied to the parent function. The coefficient −2 indicates a vertical stretch by a factor of 2 and a reflection across the xaxis.

3. Locate the vertical asymptotes. Since there is no horizontal shift or period change, the asymptotes remain at x=−π/2 x=π/2 x=(3*π)/2 etc.

4. Identify key points for one period centered at the origin. For y=−2*tan(x)

• When x=−π/4 y=−2*tan(−π/4)=−2*(−1)=2

• When x=0 y=−2*tan(0)=0

• When x=π/4 y=−2*tan(π/4)=−2*(1)=−2

5. Sketch the graph by plotting the points (−π/4,2) (0,0) and (π/4,−2) then drawing the decreasing curves between the vertical asymptotes.

Final Answer

y=−2*tan(x)

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