Graphing Techniques - Finding Possible y-values of a Curve

A sketch of the curve \(y = \frac{ax^2 + bx + c}{x + d}\) where \(a\), \(b\), \(c\) and \(d\) are constants, is shown, not drawn to scale, in the diagram.

The upper branch of the curve cuts the \(y\)-axis at the point \(A\left(0, \frac{3}{2}\right)\) and the equation of the asymptotes, also shown in the diagram, are \(x = -2\) and \(y = x - 3\).

1. Write down the value of \(d\) and determine the values of \(a\), \(b\) and \(c\).
2. Prove that \(y\) cannot take any values in the interval \((p, q)\) where \(p\) and \(q\) are constants to be determined.
3. Using the graph given and by considering the line that passes through the point of intersection of the \(2\) asymptotes, determine the range of values of \(m\) if the equation \(ax^2 + bx + c = (x + d)[m(x + 2) - 5]\) has \(2\) real roots.