Graph y=3tan(2x)

Problem

y=3*tan(2*x)

Solution

1. Identify the parent function and its properties. The function is of the form y=A*tan(B*x) where the parent function is y=tan(x)

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

P=π/2

3. Find the vertical asymptotes by setting the argument of the tangent function equal to the standard asymptotes of tan(x) which are x=π/2+n*π

2*x=π/2+n*π

x=π/4+(n*π)/2

For n=0 and n=−1 the asymptotes are x=π/4 and x=−π/4

4. Identify the vertical stretch factor. The coefficient A=3 indicates a vertical stretch by a factor of 3

5. Locate key points within one period. The center point is at (0,0) The points halfway between the center and the asymptotes are (π/8,3) and (−π/8,−3)

6. Sketch the graph by drawing the vertical asymptotes, plotting the key points, and drawing the characteristic tangent curves through those points.

Final Answer

y=3*tan(2*x)

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