Consider the following properties of a function f: f is continuous on (, 2) (2,); f(1) = 0; lim x f(x) = , limx f(x) = 3; lim x2 f(x) = , lim x2+ f(x) = ; f 0 (x) 0 when x (, 1) (3,); f 00(x) 0 when x (2, 4). Draw one possible example of a function y = f(x) that has the above properties. Point out on your graph all local extrema (and their type), asymptotes, and inflection points. Label all known x- and y-values on your axes. (You don't need to label any x- or y-values that weren't given.)

2. (4 pts) Consider the following properties of a function f: . f is continuous on (-oo, 2) U (2, 00); . f(1) = 0; . lim f(x) = -co, lim f(x) = 3; I-+00 . lim f(x) = -oo, lim f(x) = 0o; I-2 I-+2+ . f'(x) 0 when x E (-oo, 1) U (3, co); . f"(x) 0 when r E (2, 4). Draw one possible example of a function y = f(x) that has the above properties. Point out on your graph all local extrema (and their type), asymptotes, and inflection points. Label all known x- and y-values on your axes. (You don't need to label any x- or y-values that weren't given.)