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

or equivalently

B = pi/2 or -pi/2.

Thus your function has form

y=A tan(pi/2 * x -C)

or

y=A tan(-pi/2 * x -C).

If you could clarify your question or reword it, I may be able to help more.

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