Question

determine the equation in the form f(x)=1/kx-c for the function with a vertical asymptote at x=1 and a y-int at -1

Answer 1

vertical asymptote at x=1 ----> f(x) = 1/(x-1)
a y-int at -1 ----> f(x) = 1/(x-1) - 1

Answer 2

Assuming the usual sloppiness with parentheses,
f(x) = 1/(kx-c)
asymptote at x=1 means c/k = 1 so
f(x) = 1/(k(x-1))
f(0) = -1 means 1/(k(0-1)) = -1
so k = 1
f(x) = 1/(x-1)