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Lab 3 - Function Continuity Show all work on a separate sheet of paper with justifications where necessary. Answers should be clearly marked or boxed. 1. Sketch the graph of a function f with all the following properties. Identify and label any points of discontinuity on the interval (oo,00). lm f@)=-c0 lmfle)=-co lim fz)=0 z6~ lim f@)=co lm fl5)=1 f(&)=-3 2. Sketch two possible graphs of a function f that is continuous for every real number z, except & = 1, 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 z = 3, but if we redefine f at 3 so that f(3) = 2, then f becomes continuous at z = 3. 4. Determine whether the following function is continuous at @ = 9. Use the continuity checklist to justify your answers. If the function is not continuous, identify any points of discontinuity. g(z) = {:::g1 Y 18 =z=9 5. Apollo graphed the following function using Desmos, as shown below, and claimed that the function ' z2+z6 fo)= e mru is only discontinuous at the point z = 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