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Written assignments

This page will show you the best way to complete and format written assignments in my courses.
Suppose we are near the end of an algebra course, and this is the problem statement:

Assignment 12:
Find the x-intercepts of the following function.
\( f(x) = \dfrac{2x+1}{x+1} + \dfrac{3}{2x-4} \)

Content

Incorrect: Barely any work. Although it's a correct answer, I have no evidence that the problem was solved by you. Do your own work on written assignments. I grade on correct answer, correct steps, and clarity.	Correct: Sufficient balance of work and explanation. It's okay to roll a few steps into one, but be careful not to make any big jumps. See next.	Correct but overboard: Since we are in the latter part of algebra, earlier topics such as FOIL or the quadratic formula do not need thorough explanations. I will accept wordy solutions once, provided they are correct, but trim it down in the future for both our sakes! Ideally you should be able to fit your solution on one page, or two at the most.
\( f(x) = 0 \) \( -\dfrac{1}{4}, 1 \)	Assignment 12 To find the x-intercepts of f(x), I am looking for all real numbers x that solve: \( \dfrac{2x+1}{x+1} + \dfrac{3}{2x-4} = 0 \) To ensure finding all solutions and no extraneous ones, I need to add the fractions. \( \dfrac{(2x+1)(2x-4)}{(x+1)(2x-4)} + \dfrac{3(x+1)}{(2x-4)(x+1)} = 0 \) \( \dfrac{4x^2-6x-4}{2x^2-2x-4} + \dfrac{3x+3}{2x^2-2x-4} = 0 \) \( \dfrac{4x^2-6x-4+3x+3}{2x^2-2x-4} = 0 \) \( 4x^2-3x-1 = 0 \) \( (4x+1)(x-1) = 0 \) \( x = -\dfrac{1}{4}, 1 \) Both these x-values are in the domain of f(x), so they are not extraneous solutions. These are both x-intercepts of the graph of f(x).	Assignment 12 The problem says to find all the x-intercepts of f(x). So I need to find all real numbers x that solve the following equation. \( f(x) = \dfrac{2x+1}{x+1} + \dfrac{3}{2x-4} = 0 \) To ensure finding all solutions and no extraneous ones, I need to add the fractions. This is done by getting common denominators. Since \( x+1 \) and \( 2x-4 \) have no common factors, the LCM is simply their product. \( \dfrac{(2x+1)(2x-4)}{(x+1)(2x-4)} + \dfrac{3(x+1)}{(2x-4)(x+1)} = 0 \) I will use the FOIL method to expand these quadratics. \( (2x+1)(2x-4) = 4x^2 - 8x + 2x - 4 \) ... (Two full pages later...) ... \( 4x^2-3x-1 = 0 \) This is a quadratic, which means it can be solved by the quadratic formula. \( x = \dfrac{3 \pm \sqrt{(-3)^2 - 4(4)(-1)}}{2(4)} \) \( x = \dfrac{3 \pm \sqrt{25}}{8} = \dfrac{3+5}{8}, \dfrac{3-5}{8} \) \( x = 1, -\dfrac{1}{4} \) In conclusion these are the x-intercepts of f(x).

But before I can even grade content, we need to talk about...

Format

Correct formatting: You can either write or type your assignments. The above solutions are examples of correct equation formatting. (You can use LaTeX or the equation editor of your word processor.) If you write your solution, I recommend that you write in pencil to fix small mistakes now and in future attempts. You can scan or photograph it like this:	The following uploads are incorrect and will need to be reformatted and reuploaded before I can grade them on their content: Blurry, too dark/light, rotated incorrectly, too low a resolution, or otherwise unreadable.
	Unrecognized or missing filename extension (like .doc). Working formats include: pdf, png, jpg, doc, docx. Always preview your uploaded assignment to confirm it shows up.
	Typed but not equation-formatted. PLEASE do not do this! It's a migraine to interpret, and it's prone to ambiguity that can change the entire meaning of your equations. Here is one web-based equation editor, and if you remain in the sciences you will be well-served to learn the LaTeX markup language.

Upload Process

This was done on a desktop computer. Phones may behave differently or not at all.

1. On the blackboard course, open the Assignments folder. Find the assignment you are completing. Click "Start Attempt 1", then open the PDF to see the instructions.
2. When you are ready to upload, drag and drop your file into the submission box. Confirm it looks okay and click Submit. It will warn that you can’t make changes, submit anyway. I allow as many re-attempts as needed. If you click “Save” or “Save draft” but not “Submit”, I will not be able to see or grade your assignment. If days pass and you haven’t gotten a grade, this is usually why.
3. After the due date, to view your grade and feedback, open the assignment again and click on Attempt 1 (or the most recent).
4. Feedback can be found directly on the document, or to the right. If you turned in an attempt on time but got a zero, read the feedback and make corrections, and reupload the assignment by following these steps again. (Click the "Start Attempt _" button). If there is a 0 and no feedback, something went wrong. Let me know if this happens.

A note on AI

Why do I require writing? An often overlooked aspect of mathematics is accurate communication. You are arguing a case. You are solving a problem. You are walking through your thought process with someone else in order to prove to them you are correct. But most importantly, you are proving to yourself and me that you know what you're doing.

I'm aware of the tools that can solve just about any problem in our textbooks and on the online homework systems, showing all steps. Recently, machine learning (which I will call AI for the rest of this page) has made major strides. Many online tools are freely available to everyone. By this point AI can turn text prompts into pictures in seconds, carry on a conversation, and write an essay -- including a math solution. For fun I asked it to do a simple algebra problem. See how many mistakes you can spot:

Keep in mind that in all my courses, no AI or any electronics are allowed on written in-class tests.

Whatever resources you use in the meantime, whether online tutorial videos or anything not yet invented, make sure it is serving your ability to do the objectives. I design assignments to be obstacle courses to test the objectives you have just learned about. If you cannot do the obstacle course yourself, you will not be ready for the test. There is no replacement for doing the work.

AI (and other tools) would not exist without humans. They are nothing more than math. If you learn math, you will understand exactly how AI works and what its limitations are. With enough work, you will even be able to create your own models to assist you in specific goals.

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