Graph y=2tan(2x)

Problem

y=2*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 π/2+n*π

2*x=π/2+n*π

x=π/4+(n*π)/2

For the first cycle around the origin, the asymptotes are x=−π/4 and x=π/4

4. Identify the vertical stretch factor. The coefficient A=2 indicates a vertical stretch by a factor of 2

5. Determine key points within one period. The xintercept is at (0,0) Halfway between the intercept and the asymptotes, the yvalues are ±A

x=π/8⇒y=2*tan(2⋅π/8)=2*tan(π/4)=2

x=−π/8⇒y=2*tan(2⋅−π/8)=2*tan(−π/4)=−2

6. Sketch the graph by drawing the vertical asymptotes, plotting the key points (−π/8,−2) (0,0) and (π/8,2) and drawing the characteristic tangent curves through these points.

Final Answer

y=2*tan(2*x)

Want more problems? Check here!