Problem 1: Relative Asymptotic Growths (6 points) For the fo…

Problem 1: Relative Asymptotic Growths (6 points) For the following functions, order them so that if \(f_a\) appears before \(f_b\), in your sequence, then \(f_a = O(f_b)\). \(f_1 = n^3 \)\(f_2 = 1.99^n \)\(f_3 = \log^{2025} n \)\(f_4 = \tfrac{n^2}{\log n} \)\(f_5 = n \log n\) Problem 2: Asymptotic Notations (4 points) Suppose someone claims:  “The worst-case running time of Algorithm \(A\) is \(O(n^2)\), while the average-case running time is \(\Omega(n^2)\).”   Is such a situation possible? Justify your answer. Congratulations, you are almost done with Quiz 2.  DO NOT end the Honorlock session until you have submitted your work to Gradescope.  When you have answered all questions:  Use your smartphone to scan your answer sheet and save the scan as a PDF. Make sure your scan is clear and legible.  Submit your PDF to Gradescope as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.).  Click this link to go to Gradescope to submit your work: Quiz 2 Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam.  End the Honorlock session.