When graphing a tangent transformation, start by using a theta
and tan(theta) t-table for -pi/2 to pi/2. In the case of
y=Atan(Bx) or y=Atan(B(x-h)), define Bx or B(x-h) to be equal to
theta and solve for x. Now use this equation to create a x and
Atan(Bx) or Atan(B(x-h)) table, which will give coordinate pairs
to plot. The previous episode, I graphed the tangent function
between 0 and pi over 2. Now I want to extend that graph to the
left and to the right, and I'm going to need some facts from
before. First of all I have a table of values that I found
before. Tangent of 0 is 0, tangent of pi over 4 is 1 and tangent
of pi over 2 is undefined. And this is what gives us that
vertical asymptote at x equals pi over 2. I also need 2 facts.
The identity tangent of -x equals negative tangent x and that
tangent has period pi. Now this this fact means that if you take
at 2 inputs that have opposite values you get opposite outputs.
So, for example if I plug negative pi over 4 into tangent, I get
the opposite output -1.