Graph f(x)=2tan(x)

Problem

ƒ(x)=2*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 2 in front of the tangent function indicates a vertical stretch by a factor of 2 This means the yvalues of the standard tangent curve are doubled.

3. Locate the vertical asymptotes. Since there is no horizontal shift or change in period, the vertical asymptotes remain at x=−π/2 x=π/2 x=(3*π)/2 and so on.

4. Identify key points for one period between x=−π/2 and x=π/2

• At x=0 ƒ(0)=2*tan(0)=0

• At x=π/4 ƒ(π/4)=2*tan(π/4)=2*(1)=2

• At x=−π/4 ƒ*(−π/4)=2*tan(−π/4)=2*(−1)=−2

5. Sketch the curve by plotting the key points (0,0) (π/4,2) and (−π/4,−2) then drawing the characteristic tangent shape approaching the vertical asymptotes.

Final Answer

To graph ƒ(x)=2*tan(x) plot vertical asymptotes at x=π/2+n*π the xintercepts at x=n*π and use the points (π/4+n*π,2) and (−π/4+n*π,−2) to show the vertical stretch.

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