4. (19 points) Let f(x) = x2 - x + 3 (1) Find the domain of f (x). (2) Find the intercepts of f(x). (3) Determine the vertical asymptote(s); horizontal asymptote; and slant asymptote of f(x).(4) Compute f' (.12) and f\"($). (5) Give the coordinates of the critical points. (6) Find the intervals where f (2:) is increasing / decreasing. (7) Give the coordinates of the relative extrema. Classify each extrema as a relative maximum or a relative minimum. (8) Find the intervals where f(a:) is concave up / concave down. (9) Give the coordinates of any points of inection. (10) Sketch the graph of at)