Question 1 [18 Marks] Let f be the function defined by f ( x ) = 1-2x2 X2 - 1 (a) Determine the vertical and horizontal asymptotes (show all limits). (4) (b) Use the sign pattern for f (x) to determine (i) the interval(s) over which f rises and where it falls; (5) (ii) the local extrema. (c) Use the sign pattern for f to determine (i) where the graph of f is concave up and where it is concave down. (5) (ii) the inflection points (if any) (2)