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MAT135 Assignment 2

Submitting the assignment

Due date: Friday 24 September at 6pm EDT

Where to submit: On Crowdmark. You should receive an email with your personal link to the assignment on Crowdmark.

What to do: Write solutions to the problems on blank or lined sheets of paper, or write them digitally (e.g. on an iPad, but using your own handwriting). For each question, take a photo, scan, or save a file of your solutions. (You may want to start each question on a new page.) Click on the link in the email from Crowdmark, and submit your solutions one question at a time.

Notes:

1. Deadline: Deadlines to submit assignments are strict. Missing the deadline by even a few seconds will mean that you get a zero. Please give yourself lots of time to upload your assignment!

2. Time zones: Times are given in Toronto time (EST or EDT depending on the time of year). If you are in a different time zone, Crowdmark will automatically work out the time that the assignment is due. If you are unsure, log in to Crowdmark and check the assignment deadline.

3. Upload: A handwritten assignment can be scanned, or you can take a photo of it to submit. It is important that the images (e.g. the scans or photos) are clear and easy to read (not too dark or too bright, etc.) Your submitted files are what will be marked. If the Grader can’t read them, you will not get full marks. It is also OK to write your solutions using e.g. an iPad with a pen, but it should be in your own handwriting. (You should not type your solutions using LATEX.)

4. Format: Write the solution for each question on a separate page. Explain all your work, show your steps as well as your reasoning. You should write in words what you are doing and why. The person reading your solution should easily be able to understand what you have done. You will be graded on your answer, as well as your explanation of your solution.

5. Grading and feedback: The assignment is out of 15 marks: Problem 1: 5 marks. Problem 2: 3 marks. Problem 3: 1 mark. Problem 4: 4 marks. Problem 5: 2 marks Marks will depend on a combination of your answers, and your explanations. The graders may leave feedback for you on your assignment work. Please log in to Cowdmark to view the feedback. (We will announce when it is ready.)

6. Purpose: The purpose of the written assignments is to give you some practice in writing solutions to mathematical problems, without any time pressure. You will receive feedback on your writing and on your solutions. You are encouraged to take this opportunity to carefully write your solutions and think about how to best present your reasoning behind them.

7. Academic Integrity: The solutions that you submit to this assignment must be all your own work. By submitting this assignment you declare that:

(a) Your solutions are all you own work, explained in your own words.

(b) You have not copied any part of the assignment solutions from anyone or anywhere.

(c) You have not let anyone else copy any part of your solutions to the assignment.

Problems:

1. Find the domain of . Explain your work and write out all your steps as well as your reasoning. Write short sentences to explain your reasoning.

Questions 2-5: The below table lists the 20 most viewed videos on YouTube, as of September 6, 2021.

Table 1: source: https://en.wikipedia.org/wiki/List_of_most-viewed_YouTube_videos

Consider the following relations, based on the table above. Note: In each case, the domain is in the table above (videos that are not in the table are not relevant).

2. Consider the relation Y where v is the video name, and Y (v) is the Year the video was uploaded. (Note: Y (v) is the year, not the date, of upload.)

(a) What is Y (Gangnam Style)?

(b) Is Y a function? Explain why or why not.

(c) Is Y invertible? Explain why or why not.

3. Now consider the relation V where u is the name of the uploader, and V (u) is the name of the Video. Is V a function? Explain why or why not.

4. Consider the relation N where v is the video name, and N(v) is its Number in the list (for example N(Sorry) = 14).

(a) Explain how we can tell that this is an invertible function. (Note: you must explain both why it is a function, and why it is invertible.)

(b) What is N^-1 ? Explain in words what N^-1 does, and state the domain and range of N^-1. Give an example of evaluating N^-1 (choose one example value, and evaluate N^-1 of that example).

5. Using the table, find an example of a relation that is a function but that is not invertible. Explain how you know that your relation has the right properties. (Your example must be new. You can not use an example that has already been used on this assignment.)