Graphing Techniques - Sketching Rational Functions

Sketch the graph represented by each of the following equations, clearly indicating the equations of asymptote(s), axial intercept(s), and the coordinates of the turning point(s), if any.

1. \(y = 2x^3 - 5x^2 + x - 2\)
2. \(y = 4x^2 e^x\)
3. \(y = \frac{\ln x}{2x}\)
4. \(y = \frac{x^2 + 2x - 8}{x^2 + 2x - 3}\)
5. \(y = |2x - x^2|\)
6. \(y = \frac{ax + 1}{x - b}\), where constants \(a\), \(b\) are given by
   1. \(-1 < a < 0\) and \(0 < b < 1\);
   2. \(a < -1\) and \(b > 1\).

What could be said about the graph if \(ab + 1 = 0\)?