Hui Lab 3 - Function Continuity Show all work on a separate sheet of paper with justifications where necessary. Answers should be clearly marked or boxed. Print first and last names of each group member at the top of the page. 1. Sketch the graph of a function f with all the following properties. Identify and label any points of discontinuity on the interval (-0o, co). lim f(x) = 00 lim f(x) = 00 lim f(x) = 6 x-+2+ lim f(x) =-00 2+-4+ lim f(x) = 1 f(2) = -1 2+2- 2. Sketch two possible graphs of a function f that is continuous for every real number r, except x= -4, at which point f is continuous from the right. What type of discontinuity is produced in this scenario? Explain your answer. 3.) Give two possible examples of a function f that is not continuous at a = 1, but if we redefine f at 1 so that f(1) = 2, then f becomes continuous at $ = 1. 4. Determine whether the following function is continuous at a = 5. Use the continuity checklist to justify your answers. If the function is not continuous, identify any points of discontinuity. 9(z) = 2-25 x # 5 10 x =5 5. Apollo graphed the following function using Desmos, as shown below, and claimed that the function f(z) = - x2 +x-6 2 - 9x + 14 is only discontinuous at the point a = 7. (a) Is Apollo correct? (b) Do any other points of discontinuity exist, and if so explain why they are not shown on the graph