Question

3. Sketch the graph y = f(x) of a function f, which has all of the following properties. (Note that you are not being asked to give an explicit formula for .) (i) f is an odd function. (ii) / has exactly one root (z-intercept). (iii) The domain of / is the entire real line. (iv) f() has a global (absolute) maximum at x = 2 and this is the only extremum (absolute or relative) of f(c) for all values >0. (v) The graph off is a continuous curve. (vi) The z-axis is a horizontal asymptote off.