Graph y=5tan(x)

Problem

y=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. The coefficient 5 indicates a vertical stretch by a factor of 5 This means the points that are normally at (π/4,1) and (−π/4,−1) on the parent graph will be shifted to (π/4,5) and (−π/4,−5)

3. Identify key points for one period centered at the origin. The graph passes through the origin (0,0) As x approaches π/2 from the left, y approaches ∞ As x approaches −π/2 from the right, y approaches −∞

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

5. Sketch the curve. Draw the characteristic tangent shape passing through (−π/4,−5) (0,0) and (π/4,5) ensuring the curve approaches the vertical asymptotes without touching them.

Final Answer

y=5*tan(x)

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