Graph y=2tan(x/4)

Problem

y=2*tan(x/4)

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

2. Determine the period of the transformed function. The period P is calculated by dividing the period of the parent function by the coefficient of x

P=π/(1/4)

P=4*π

3. Find the vertical asymptotes by setting the argument of the tangent function equal to the locations of the parent function's asymptotes.

x/4=π/2

x=2*π

x/4=−π/2

x=−2*π

The asymptotes occur at x=2*π+4*n*π

4. Identify key points within one period centered at the origin.
   When x=0

y=2*tan(0)=0

When x=π

y=2*tan(π/4)=2*(1)=2

When x=−π

y=2*tan(−π/4)=2*(−1)=−2

5. Sketch the graph by plotting the points (−π,−2) (0,0) and (π,2) then drawing the tangent curves approaching the vertical asymptotes at x=−2*π and x=2*π

Final Answer

y=2*tan(x/4)

The graph has a period of 4*π vertical asymptotes at x=±2*π and passes through (−π,−2) (0,0) and (π,2)

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