Is the function continuous for all x ? If not, say where it is not continuous and explain in what way the definition of continuity is not satisfied. f ( x ) = x x # 0 1 x = 0 K O f(x) is not continuous for all x because lim f (x) does not exist. x-0 O f(x) is not continuous for all x because f(x) is not defined at x = 0. O f (x) is not continuous for all x because lim f (x) does not exist. x-0 O f(x) is continuous for all x because f(x) is defined for all x and lim f (x) = 1. x-0 O f(x) is continuous for all x because f (x) is defined for all x and lim f (x) = 0. x -+0