Use the intermediate value theorem to show that x5 - 3x3 - 2x + 4 = 0 has at least one real solution, and determine an interval in which this solution lies. Sketch the graph of a function f exhibiting the following behaviour: . The domain of f is [0, 5]. The range of f is (0, 2) U {4} U [5, 10] . f is continuous on (0, 2) U (2, 4) U (4, 5). . f is not continuous at the points x = 2 and x = 4. lim f (x) = 2. I 2 . lim f(x) does not exist. 1-+4 . f is continuous from the left at both x = 4 and x = 5. . f is not continuous from the right at x = 0