# Thread: Graphing Periods, Asymptotes and End Points

1. ## Graphing Periods, Asymptotes and End Points

So the problem states to graph one complete period for f(x) = tan(3x - pi/2).

So that becomes f(x) = tan 3(x - pi/6).

Period = pi / 3
Phase shift = pi / 6

How do I get the end points / asymptotes? This is a pretty easy question, but I must not be getting something.

I have the answers as x = 0, and x = pi / 3.

I also see that for a basic curve, the end points are x = -pi / 2, and x = pi / 2, and when it shifts they become x = 0 and x = pi / 3.

Thank you for helping me on this easy problem

2. Originally Posted by NYKnicks
So the problem states to graph one complete period for f(x) = tan(3x - pi/2).

So that becomes f(x) = tan 3(x - pi/6).

Period = pi / 3
Phase shift = pi / 6

How do I get the end points / asymptotes? This is a pretty easy question, but I must not be getting something.

I have the answers as x = 0, and x = pi / 3.

I also see that for a basic curve, the end points are x = -pi / 2, and x = pi / 2, and when it shifts they become x = 0 and x = pi / 3.

Thank you for helping me on this easy problem
1 period of $y = \tan{x}$ is from $-\frac{\pi}{2} < x < \frac{\pi}{2}$

period transforms from $\pi$ to $\frac{\pi}{3}$

period for $t = \tan(3x)$ is from $-\frac{\pi}{6} < x < \frac{\pi}{6}$

shift the above period to the right $\frac{\pi}{6}$ units ...

$-\frac{\pi}{6} + \frac{\pi}{6} < x < \frac{\pi}{6} + \frac{\pi}{6}
$

new period ...

$0 < x < \frac{\pi}{3}$