1. Consider the function f(x) = -1+ 2x2 3(1 + 2 2 ) (a) Find the natural domain of f and its vertical and horizontal asymptotes, if any. (b) Find the x-intercept(s), the critical point(s), and point(s) of inflection of f (x). (c) Find the values of x for which f is decreasing and the values for which f is in- creasing. Determine the nature of the critical point(s) of f. (d) Sketch the graph of f, showing all the features found in Parts (a), (b) and (c). (e) Find the global maximum and the global minimum of f in the interval [-1, 2]