Graph y=-5tan(x)

Problem

y=−5*tan(x)

Solution

1. Identify the parent function as 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 −5 indicates a vertical stretch by a factor of 5 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 and x=π/2 for one cycle.

4. Find the key points for one period. The center point is at (0,0) For y=−5*tan(x) the points at the quarter-period intervals are (π/4,−5) and (−π/4,5)

5. Sketch the curve. Start at the left asymptote x=−π/2 pass through (−π/4,5) (0,0) and (π/4,−5) then approach the right asymptote x=π/2 Because of the negative sign, the graph decreases from left to right.

Final Answer

y=−5*tan(x)

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