Graph f(x)=1/2*tan(x)

Problem

ƒ(x)=1/2*tan(x)

Solution

1. Identify the parent function and its properties. The parent function is 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 transformation applied to the parent function. The factor of 1/2 in ƒ(x)=1/2*tan(x) represents a vertical compression by a factor of 2

3. Find the vertical asymptotes of the function. Since the horizontal scale is not changed, the asymptotes remain at x=−π/2 x=π/2 x=(3*π)/2 and so on.

4. Identify key points for one period. For the interval (−π/2,π/2) the center point is (0,0) The points at x=−π/4 and x=π/4 are scaled by 1/2

ƒ*(−π/4)=1/2*tan(−π/4)=−1/2

ƒ(0)=1/2*tan(0)=0

ƒ(π/4)=1/2*tan(π/4)=1/2

5. Sketch the graph by plotting the key points (−π/4,−0.5) (0,0) and (π/4,0.5) then drawing the characteristic tangent curves between the vertical asymptotes.

Final Answer

ƒ(x)=1/2*tan(x)

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