Graph y=tan(4x)

Problem

y=tan(4*x)

Solution

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

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

P=π/4

3. Find the vertical asymptotes by setting the argument of the tangent function equal to the standard asymptote locations of π/2+n*π

4*x=π/2

x=π/8

4*x=−π/2

x=−π/8

4. Identify the x-intercept for one cycle. Since there is no horizontal or vertical shift, the graph passes through the origin.

(0,0)

5. Determine key points between the intercept and the asymptotes. For y=tan(4*x) the function reaches y=1 and y=−1 at one-quarter and three-quarters of the way through the period.

x=π/16⇒y=tan(π/4)=1

x=−π/16⇒y=tan(−π/4)=−1

6. Sketch the graph by drawing the vertical asymptotes at x=±π/8 plotting the points (−π/16,−1) (0,0) and (π/16,1) and drawing the characteristic tangent curve increasing from left to right between the asymptotes.

Final Answer

y=tan(4*x)* has period π/4* and asymptotes at *x=π/8+(n*π)/4

Want more problems? Check here!