Graph y=7tan(x)

Problem

y=7*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. The coefficient 7 indicates a vertical stretch by a factor of 7 This means the points that are normally at (π/4,1) and (−π/4,−1) on the parent graph will be shifted to (π/4,7) and (−π/4,−7)

3. Identify the intercepts and asymptotes. Since there is no horizontal or vertical shift, the xintercepts remain at x=n*π (e.g., (0,0) (π,0). The vertical asymptotes remain at x=π/2 and x=−π/2

4. Sketch the graph. Draw the vertical asymptotes as dashed lines. Plot the origin (0,0) and the guide points (π/4,7) and (−π/4,−7) then draw the characteristic tangent curve through these points, increasing from left to right between the asymptotes.

Final Answer

y=7*tan(x)

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