(-00, -3) -3 (-3, -1) -1 (-1, 0) (0, 1) 1 (1, +00) f'x + und und f"x + und und + +

Consider the function f that is continuous everywhere except at x = 0 and whose only intercept point is (−1, 0). Moreover, suppose that f (−3) = f (1) = −1, lim x→0 f (x) = −∞, and                   lim x→+∞ f (x) − (1 − x)] = 0. The table of signs for f' and f'' is given.

1. Give equations of the two linear asymptotes of the graph of f. 

2. Determine where is f increasing or decreasing, and where is f concave up or concave down. Give the coordinates of the relative extremum point (identify whether it is a relative maximum point or a relative minimum point) and of the inflection point of the graph of f.

3. Sketch the graph of f with emphasis on the concavity. Label all the intercept points, relative extremum points, and inflection points with their respective coordinates, and the asymptotes with their respective equations