Graph y=tan(1/2x)

Problem

y=tan(1/2*x)

Solution

1. Identify the parent function and its properties. The function is in the form y=a*tan(b*x) where a=1 and b=1/2

2. Determine the period of the function. The period of a tangent function is calculated using the formula P=π/|b|

P=π/(1/2)

P=2*π

3. Find the vertical asymptotes by setting the argument of the tangent function equal to the standard asymptotes of tan(θ) which are ±π/2

1/2*x=−π/2⇒x=−π

1/2*x=π/2⇒x=π

4. Identify key points within one period. The x-intercept occurs at the center of the period, and the function reaches y=±1 at the quarter-period marks.

x-intercept:(0,0)

Point 1:(−π/2,−1)

Point 2:(π/2,1)

5. Sketch the graph by drawing the vertical asymptotes at x=−π and x=π plotting the key points, and drawing the characteristic tangent curve that increases from left to right.

Final Answer

y=tan(1/2*x)

The graph has a period of 2*π vertical asymptotes at x=π+2*π*k for any integer k and passes through (0,0) (π/2,1) and (−π/2,−1)

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