The function f is of the form \(f(x) = \frac{{x + a}}{{bx + c}}\), \(x \ne - \frac{c}{b}\). Given that the graph of f has asymptotes x = −4 and y = −2 , and that the point \(\left( {\frac{2}{3},{\text{ }}1} \right)\) lies on the graph, find the values of a , b and c .

vertical asymptote \(x = - 4 \Rightarrow - 4b + c = 0\)     M1

horizontal asymptote \(y = - 2 \Rightarrow \frac{1}{b} = - 2\)     M1

\(b = - \frac{1}{2}{\text{ and }}c = - 2\)     A1A1

\(1 = \frac{{\frac{2}{3} + a}}{{ - \frac{1}{2} \times \frac{2}{3} - 2}}\)     M1

\(a = - 3\)     A1

[6 marks]