Question

What is the equation for the vertical asymptotes of the function f(x)=-3tan(0.5x)?

Answer 1

I have one equation being y=2npi+pi is this right?

Answer 2

Well, do you know the normal period of the tangent function?

Answer 3

pi

Answer 4

Right. And do you know where the tangent asymptotes normally are?

Answer 5

y=(npi/2)

Answer 6

Alright, well when you have a function atan(bx + c), the new period of the function is pi/b. So in this case, your b is .5, making your new period 2 pi. Now as for where your asymptotes start from. We have two asymptoes, one at -pi/2 and the other at pi/2. Now we make an inequality with our tangent angle in between these two asymptotes like this:
\[-\frac{ \pi }{ 2 }\le.5x \le \frac{ \pi }{ 2 }\] Now we solve for x and that will give us two asymptotes from which we can add our period on to to get all of our asymptotes.

Answer 7

y=npi? is the asympyotes?

Answer 8

Your asymptotes start at -pi and then add 2npi. because 2pi is our new period.

Answer 9

Oh!! I get it! Thanks!

Answer 10

Awesome xD Np :3