*Analyze f(x)*.- Find the domain of
*f*. - Find the intercepts.
- Find asymptotes.

- Find the domain of
*Analyze f'(x)*.- Find the partition numbers for
*f'*and the critical numbers of*f*. - Construct a sign chart for
*f'(x)*. - Determine the intervals on which
*f*is increasing and decreasing. - Find the local maxima and minima of
*f*.

- Find the partition numbers for
*Analyze f''(x)*.- Find the partition numbers for
*f''*. - Construct a sign chart for
*f''(x)*. - Determine the intervals on which the graph of
*f*is concave upward and concave downward. - Find the inflection points of
*f*.

- Find the partition numbers for
*Sketch the graph of f*.- Draw asymptotes and locate intercepts, local maxima and minima, and inflection points.
- Sketch in what is known from steps 1 - 3.
- Plot additional points as needed and complete the sketch.

If a graph approaches a line that is neither horizontal nor vertical as *x* approaches ∞ or -∞, then that line is called an **oblique asymptote**.