Vertical asymptote at -4/3 means x+4/3 in the denominator
x intercept at (-1, 0) means x+ 1 in the numerator
hole at 1/2 means
x- 1/2 in numerator and denominator, or 2x - 1 in both places
Thus, we start with c(x+1)(2x-1)/((x+4/3)(2x-1))
At 1/2, we have a limit of c(x+1)/(x+4/3) = c(1/2+1)/(1/2+4/3) = 3/2c/(11/6) = 3/2c * 6/11 = 9c/11
As the hole is (1/2, 3/11) 9c/11 = 3/11 or c = 1/3
This is wonderful news, as the horizontal asymptote equals c
Thus, our function is 1/3 (x+1)(2x-1)/(x+4/3)(2x-1)) =
(x+1)(2x-1)/(3(x+4/3)(2x-1)) =
(x+1)(2x-1)/((3x+4)(2x-1) =
(2x^2 +x-1)/(6x^2+5x-4)
