Sketch the graph of a function f such that (a) to (k) below hold. For full...

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Sketch the graph of a function f such that (a) to (k) below hold. For full marks clearly and carefully label all intercepts, relative extrema, inflection points, and asymptotes. (a) Domain: (-, ). (b) Continuous for all real numbers. (c) Differentiable everywhere except at x = -3. (d) f(0) = 6. (e) lim f(x)=0. 81x (f) f'(-2)= f'(0) = 0. (g) f'(x) <0 on (-00, -3) and (0,). (h) f'(x)0 on (-3,0). (i) lim f'(x): = and lim f'(x)=-. (-3)+ x-(-3)- (j) f"(x)>0 on (-2, -1) and (2,). (k) f"(x) < 0 on (-00, -3), (-3, -2) and (-1,2). Sketch the graph of a function f such that (a) to (k) below hold. For full marks clearly and carefully label all intercepts, relative extrema, inflection points, and asymptotes. (a) Domain: (-, ). (b) Continuous for all real numbers. (c) Differentiable everywhere except at x = -3. (d) f(0) = 6. (e) lim f(x)=0. 81x (f) f'(-2)= f'(0) = 0. (g) f'(x) <0 on (-00, -3) and (0,). (h) f'(x)0 on (-3,0). (i) lim f'(x): = and lim f'(x)=-. (-3)+ x-(-3)- (j) f"(x)>0 on (-2, -1) and (2,). (k) f"(x) < 0 on (-00, -3), (-3, -2) and (-1,2).