Sketch the graph of a function f(x) that has the following properties. Identify and label all asymptotes in your graph. (Use of pencil or another erasable writing method is highly recommended! You may need to backtrack quite a lot while doing this problem.): . The domain of f is R y = -2 is an asymptote of f. . lim f(x) does not exist H--3 f is right-continuous at x = -3 f(1) = 5 f has an infinite discontinuity at x = 1 f is increasing on the interval (1,4) . f is decreasing on the interval (4,00) lim f(x) = 2 818 Let f(x) be a function with the following properties: f(x) is continuous at least on the interval [0, 4] (possibly elsewhere too) . Some of the values of f(x) are given in the table below: I 4 5 0 1 2 3 f(x) 06 15 6 15 15 100 270 (a) Based on the information given, what is the minimum number of solutions that the equation f(x) - 3 = 4 could have in the interval (0,4)? For each solution, indicate the smallest interval in which that solution in which that solution is known to occur. (b) Is there guaranteed to be a solution in the interval (4,5)? Explain in English sentences why or why not. |x + 1 (a) Find the equations of all asymptotes of the function f(x)= to justify, in terms of limits, why a particular line is an asymptote. = 2x - 3 Be sure (b) Design a continuous function g(x) so that lim g(x) = -2 and_lim_g(x) = 0. 81X 8118 (c) How many different horizontal asymptotes can a function have?