7 A curve has equation \(y = \frac { ( 2 x - 3 ) ( x + 1 ) } { ( x + 4 ) ( x - 2 ) }\).
- Write down the values of \(x\) for which \(y = 0\).
- Write down the equations of the three asymptotes.
- Determine whether the curve approaches the horizontal asymptote from above or from below for
(A) large positive values of \(x\),
(B) large negative values of \(x\). - Sketch the curve.
- Solve the inequality \(\frac { ( 2 x - 3 ) ( x + 1 ) } { ( x + 4 ) ( x - 2 ) } \leqslant 2\).