Graph y=tan(2x)

Problem

y=tan(2*x)

Solution

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

2. Determine the period of the function. The period P is calculated by dividing the base period by the coefficient of x

P=π/2

3. Find the vertical asymptotes by setting the argument of the tangent function equal to the standard asymptote locations for tan(x) which are 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 x-intercepts by setting the function equal to zero. The intercepts occur halfway between the asymptotes.

2*x=n*π

x=(n*π)/2

For n=0 there is an intercept at (0,0)

5. Plot key points to determine the shape. Evaluate the function at x=π/8 and x=−π/8

y=tan(2⋅π/8)=tan(π/4)=1

y=tan(2⋅−π/8)=tan(−π/4)=−1

6. Sketch the graph by drawing the vertical asymptotes at x=±π/4 plotting the intercept at the origin, and drawing the characteristic increasing tangent curves through the key points.

Final Answer

y=tan(2*x)

The graph has a period of π/2 vertical asymptotes at x=π/4+(n*π)/2 and passes through (0,0) (π/8,1) and (−π/8,−1)

Want more problems? Check here!