For this rational function: f(x) = 4x^3 - 8x^2 + 2x + 5/x^4 + 2x^3 - 7x^2 - 8x + 12,

1. A complete analysis of the function i.e. state the domain, range, x-intercept(s), y-intercept, vertical asymptote(s), horizontal/oblique asymptote.

2. What happens to the curve as it approaches the vertical asymptote(s)?

3. Determine the end behaviour of the function. Does the curve approach the horizontal/oblique asymptote from above or below?

4. Set up an inequality and state the intervals of positivity/negativity using the Chart (Factor table) Method.

5. Graph the function.