i need help solving my home work with work shown

Rutgers University-Camden 640:121 Unified Calculus I Assignment 1.8 1. Define g to be the function 212 - 5x - 3 g(]) = I - 3 if x / 3 if x = 3 (a) Sketch a graph of g. (b) Determine any values where g is discontinuous and explain why. 2. Let f be given by f(x) = sin ifI 3 Determine the values of a and b that make f continuous everywhere. 4. Use the Intermediate Value Theorem to show that sinn = r' - r has a solution on the interval (1, 2). 5. Show that the equation 2v/7 -1 - VI = 3 has a solution. 6. Assume that f is continuous on [0, 1] and that f(0) = 2 and f (1) = 1. Show that the graph of y = f(r) must intersect the graph of y = I' + 1 at least once on the open interval (0, 1). 7. Consider g(x) = 1 +5 I _ 2 on the interval [1, 4]. (a) Show that g(1) 0. (b) Explain why, in this case, it is NOT valid to use the Intermediate Value Theorem to conclude that there exists a ce (1, 4) such that g(c) = 0