Course talk:MATH110/003/Groups/Group 06

Dear group 6,

First of all, your group page is a huge mess. The way you handled titles makes homework 3, 4, 5, 7 subparts of the Piecewise part. Please reorganize your content in a more structured way. You're welcomed to create subpages (as you already did) and put the content elsewhere if you want to, but right now it's way to messy.

Now, a few remarks about your part on piecewise functions.

• Your definition on what is a piecewise function can be improved a lot:
  • I have nothing against adding a picture, but it's barely legible and the quality cannot be improved right now, so it's really hard to read.
  • Your first example uses a function which has a vertical asymptote, is it really the best thing to show as a first example? It might be confusing as a first example, but could be a good example later to show the function could be broken in three parts but look as if it had four parts.
  • Speaking of that example, you draw a function that has a vertical asymptote at x=1/2, but it seems to me that the function you gave has a vertical asymptote at x=-1/2. So basically, your picture doesn't match your function...
  • Furthermore, your picture now shows a function which is not defined at x=1/2, it would be interesting to discuss the issue of the domain a little bit. On your picture, the function doesn't take any value at x=1/2, but it seems it should take one when we look at the function itself. Things to say again. Remember, the goal is to clarify the topic for the other students as much as possible.
• It is interesting to have a discussion about what piecewise functions are good for. I think it could be improved by expanding a little bit and giving examples. Also, why is that discussed in the what is it? part?
• I find it amusing that in the how to graph them section we don't see any graph. Something to improve I think.
• Which leads me to two technical suggestions:
  • To graph piecewise functions, wolfram alpha can do a good job for you. An easy google search gave me the following link that tells you how to input this in WolframAlpha. You can get something like this and then save the picture and upload it on the wiki.
  • To write piecewise function in the wiki, you can use the latex environment cases the idea is that inside the environment cases that you start with a begin and an end you can write stuff, then the & symbol creates a tabulation and then you go to the next line by adding a double backslash \\ and so on. It looks like this:

Input	Output
<math>f(x) = \begin{cases} x+2 & x \leq 1\\ x^2-3x & x>1 \end{cases}</math>	$f(x)={\begin{cases}x+2&x\leq 1\\x^{2}-3x&x>1\end{cases}}$

• • You can embed your YouTube videos directly in the wiki (it's much more cool). To know how, check the corresponding help page.
• I also really like the idea of the problems you mention about differentiability and continuity. It's by far optional, but there is definitively some interest there. This could be a good opportunity to earn bonus points if you have the time to work on it.

Thanks for all the work so far, looking forward to your updates and upgrades. Feel free to contact me if needed.

Cheers,

Dear group 6,

Good job at taking my remarks in account, the page looks way better now. Think of what could improve your page for the other students while they browse it. Making it as user friendly as possible is really what will decide if it's useful or not. A few suggestions:

• Write a more detailed description of the youtube videos. What would a student really gain by watching it?
• In your how to modify them section, your piecewise function isn't defined at 1. Is that intended? It doesn't feel like that to me. I think one of your < or > sign should become a $\leq$ or $\geq$.
• Speaking of that problem, it would be interesting to graph a few of these functions for different values of a to get a feeling of what finding THE good value of a means.
• A format issue, in that same problem, why do you have brackets around your big fraction? Does that really add anything?
• Showing the graph of a step function could be great to visualize things.
• Your bit on continuity seems interesting, but definitively needs more work.

Cheers,

Dear group 6,

The TA and I have reviewed your work. Here are our assessment of your work.

• Presentation: Very good organization, very readable, document looks like a whole and section transitions nicely.
• Mathematical content: There was a ""what does this mean?"" under section Differentiability in Regards to Piecewise Functions, seems unfinished? But good to explore into calculus. Overall the information provided are accurate and complete.
• Overall perceived effort: Good efforts over all.

Good job everyone! All the questions are very nicely done. Just to say that perhaps you could distinguish the problem from the solutions more clearly, say, in problem 1 for example. Other than that, it's a well organized and well answered paper!

Good job in sticking to a consistent format! A quick point though: it would make it easier to read if you separate the questions and answers into different paragraphs or use different font/bold, right now it's all scrambled together and difficult to read. A few more pointers for improvement:

• More thought process is needed for some questions! For example, just writing "write this into a system of equations and solve it" isn't going to cut it. Give your procedures! Writing out equations in words is not bad in itself(and I'm not taking marks off for that), but perhaps write it in mathematical notation would make the "equations" referred to more clear to the reader.

• Read questions more carefully! Give it a little more thoughts! Check your answers to see if they are logical! This golden rule never fails!