Can you please help me solve those 2 questions (Find a function y = f(x) which has only one horizontal asymptote and exactly 2021 vertical asymptotes. You have to clearly write the formula for f(x) for and explain carefully why your function satisfies the given condition. A sketch of the graph is recommended but it is not enough for your explanation.

6. Consider the function f(x) = 2-MI ifI CO if I > 0 (a) (2 marks) Is f(r) continuous at r = 0? Justify your answer with calculations. (b) (3 marks) Now consider the function g(x) - MI if r S a if r > a Show that there exists a value of a which makes g(r) continuous everywhere. (Hint: Draw the graphs of y = 2 - xx and y = x on the same axes. For a particular value of a, the graph of g(x) looks like y = 2 - ar for r a. Based on the graphs, how should you choose a so that g(r) is continuous? Use the IVT to justify that there is such a number a.)