Make a rational equation that have vertical asymptotes of x = -3 and x = 6, oblique/slant asymptote of y=x+2, and goes through points (0,4), (1,2), and (4,2)

Answer 1

f(x) = (x³ + ax² + bx + c)/[(x + 3)(x - 6)];

f(0) = c/(-18) = 4; c = - 72; f(1) = (1 + a + b - 72)/(-20) = 2; a + b = 31;

f(4) = (64 + 16a + 4b - 72)(-14) = 2; 16a + 4b = - 20; 4a + b = - 5; a = - 12; b = 43;

f(x) = (x³ - 12x² + 43x - 72)/[(x + 3)(x - 6)]

I think that y = x - 9 is slant. To many conditions