Question

How do I find the formula of a rational function graph with this information: asymptotes: x=-6 x=1 and then point (2,-1/4)

Answer 1

A hint would be that asymptotes can appear where the function is undefined (the denominator is 0). In this problem asymptotes are required at two points. Something like (x+6) in the denominator gives an asymptote at x = -6 and likewise (x+1) would handle x=1. You could write this as y = C/((x+6)(x-1)) to get a family of rational functions with the desired asymptotes, changing the value of C will move the curve but not the asymptotes. Then using the extra information (2,-1/4) you can solve for C. Now (-1/4) = C/((2+6)(2-1)) leads to C = -2. So one possible function would be
y = -2/((x+6)(x-1)