2. Consider the function CU f($) : ($_ 1)2' What is the natural domain of this function? What is the range of f (:13) over its natural domain? Find lim f (30) and lim f(ac). $)OO 56)00 Are there any a E R such that lim f(:c) = 00 or lim f(:c) = 00? {II)0) {IIH1 Find f'(:c) and nd a: and f (2:) at any critical points. Use f'(m) to nd where f (:13) is increasing and where f (x) is decreasing. Find f"(ac) and use this to nd where the curve y = f($) is concave up and where y = f (a?) is concave down. Use the above information to produce a handdrawn sketch of the curve y : f (33). On your sketch, label any notable features of the curve, including any local maxima and minima, points of inection. Give the coordinates of each of these points. Label any horizontal and vertical asymptotes. Clearly show the value of y at the y intercept (where the curve crosses the yaxis)