Graph y=tan((pix)/2)

Problem

y=tan((π*x)/2)

Solution

1. Identify the parent function and its properties. The function is of the form y=tan(B*x) where B=π/2

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

P=π/π/2

P=2

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

(π*x)/2=π/2

x=1

(π*x)/2=−π/2

x=−1

The vertical asymptotes occur at x=1+2*n for any integer n

4. Identify key points within one period (−1,1)
   At x=0 y=tan(0)=0
   At x=0.5 y=tan(π/4)=1
   At x=−0.5 y=tan(−π/4)=−1

5. Sketch the graph by drawing the vertical asymptotes at x=−1,1,3,… and plotting the points (0,0) (0.5,1) and (−0.5,−1) then drawing the characteristic tangent curves increasing from left to right between each pair of asymptotes.

Final Answer

y=tan((π*x)/2)

The graph is a periodic tangent curve with a period of 2 vertical asymptotes at x=…,−1,1,3,… and xintercepts at x=…,−2,0,2,…

Want more problems? Check here!