graph y = Atan(Bx-c) with y-coordinates on graph 1/4 and 3/4 between consecutive asymptotes -1 and 1
I do not think there is enough information provided. What I can tell you is that if your tangent function has consecutive tangent at x=-1 and x=1, then your period is 2.
Recall that the period of the function y=A tan(Bx-C) is pi/abs(B). Since pi/abs(B) = 2, then
abs(B) = pi/2
B = pi/2 or -pi/2.
Thus your function has form
y=A tan(pi/2 * x -C)
y=A tan(-pi/2 * x -C).
If you could clarify your question or reword it, I may be able to help more.