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Graph y=-3tan(x)

Problem

y=−3*tan(x)

Solution

  1. Identify the parent function and its properties. The parent function is y=tan(x) which has a period of π vertical asymptotes at x=π/2+n*π and passes through (0,0)

  2. Determine the transformations applied to the parent function. The coefficient −3 indicates a vertical stretch by a factor of 3 and a reflection across the xaxis.

  3. Find the vertical asymptotes. Since there is no horizontal shift or period change, the asymptotes remain at x=−π/2 and x=π/2 for one cycle.

  4. Identify key points for one period. For y=−3*tan(x) calculate values at specific x coordinates:

  • At x=−π/4 y=−3*tan(−π/4)=−3*(−1)=3

  • At x=0 y=−3*tan(0)=0

  • At x=π/4 y=−3*tan(π/4)=−3*(1)=−3

  1. Sketch the graph by plotting the points (−π/4,3) (0,0) and (π/4,−3) then drawing the curve approaching the vertical asymptotes. Because of the reflection, the graph decreases from left to right between asymptotes.

Final Answer

The graph of y=−3*tan(x) is a periodic curve with vertical asymptotes at x=π/2+n*π passing through (0,0) (−π/4,3) and (π/4,−3)

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