Homework-Helpers

Hey everyone, so I work at an academic library and today I’ve launched a personal Discord server to offer help to students who need library reference and research help. (You’ll see me in-server with the nickname “J.P. Armitage.”)

I have Discord running on my desktop in the background pretty much sixteen hours a day, seven days a week right now, so if you need help figuring out a database, finding peer-reviewed articles, want someone to give you quick thoughts on a paper, etc., I may be able to help.  I don’t expect it to be a high volume server, but I’m offering it to our students during the current social distancing conditions because our physical facility is closed, and thought I would offer it to you out there as well.  DM me if the invite link has expired by the time you want it. Cheers! 

Hey, also, please consider sharing this with any students you know who might could use the help.

(x-n)/(x-n) makes a hole at x=n because, for x=n, there is a zero in the denominator, and as everyone knows, you can’t divide by zero. To explain this fully, let’s graph the function y=(x-2)/(x-2). As you can see from the graph, (x-2)/(x-2) is equal to 1 everywhere except for x=2 where it is undefined (you can use the table function or check the value at x=2 by hovering over the point in Desmos to verify this). 

So, when you multiply anything by 1, you get the same thing, and when you multiply something by ‘undefined,’ you get ‘undefined,’ which is represented on a graph as a hole because no value is returned by the function. This means that when you multiply a function by (x-n)/(x-n), you get the exact same function everywhere except x=n, where you get undefined, which again causes a hole in the graph. 

As to why you can’t ‘cancel’ the (x/n)s, the answer is complicated. The short answer is that it’s a function. Because there is not a single answer, every operation must be done in a way that does not hide or eliminate information, specifically zeroes in the denominator. Here’s why: canceling something in the numerator and denominator only works because it is the same as saying the two expressions are equal, ie 2/2*5=5. However, the same cannot be said for functions which cause zeroes in the denominator because (x-2)/(x-2) *is not equal to 5 when x=2 (because it’s undefined). I know this feels like circular logic, but it’s the best way to explain it.

– Admin Noah

(Warning, this post quickly grew out of my control. Excessive chemistry and explanation below.)

i have been trying to finish my degree for seven years now and i'm SO CLOSE, but i have to write a 3.5k essay on an empirical linguistics question of my choosing by tomorrow evening. i would like to write about the "because"-as-a-preposition/noun/something-new phenomenon (e.g. "because feelings") with examples from twitter+tumblr, but i can't for the life of me come up with a research QUESTION.