Limits and Continuity Discussion-Based Assessment Assigned Problems 1. Let f be the function given by f(x) = 2x VX2 - 1 Part A: What is the domain of f? Part B: Find the range of f. 3x2 + 10x - 8 for X 2 Part A: For what value of k, if any, is f continuous at x = -4? Justify your answer. Part B: Find all asymptotes to the graph of f. Show the work that leads to your answer. 3. The functions fand g are continuous for all real numbers, and g is strictly increasing. The table gives values of the functions at selected values of X. X f(x) g(x) 2 3 -6 3 5 2 6 -12 3 9 -4 6 The function h is given by h(x) = f(g(x)) - 3. Explain why there must be a value / for 3 0 3x Part B: lim x +4 X4X +4 5. Use the graph of f(x) and g(x) to find each of the following limits (if it exists). f ( x ) g(x) yT 3 3 2 2 O -1 -1 -2 -2 -3 -3 -2 AA -3 =2 -1 2 3 Part A: lim[f(x).9(x)] Part B: lim[f(x) . g(x)] X->2 Part C: lim[f(x) + 29(x)] X >-1 Part D: lim g(f(x)) X - -3