(2x +1 if x1 2. Explain why f (x) =13 -x2 if x > ] Is discontinuous at x = 1. Is it a removable, jump, or infinite discontinuity? (Explain why). 3. Let f(x) = 2x3 - 7x2 + x + 3. Show that f (x) has a root in the interval [0, 3] using the Intermediate Value Theorem. Check each hypothesis of the theorem and explain why it applies. 4. Sketch the graph of a function f that has the following: -5 -3 -2 -1 0 +-X a) Has a removable discontinuity at x = -3. -4 1 2 3 4 5 b) Has a jump discontinuity at x = 0. c) Has an infinite discontinuity at x = 3. d) It is continuous everywhere else. 4