The graph of $y = \frac{p(x)}{q(x)}$ is shown below, where $p(x)$ and $q(x)$ are quadratic. (Assume that the grid lines are at integers.)

The horizontal asymptote is $y = 2,$ and the only vertical asymptote is $x = -2.$ Find $\frac{p(3)}{q(3)}.$

maximum Aug 28, 2023

#1**0 **

I suppose I will ignore the fact that the given diagram does not match the description given of this arbitrary rational function. The written words state that x = - 2 and y = 2 act as the only asymptotes, yet the diagram shows that x = 2 and y = 1 are the asymptotes.

Despite this, I noticed that there is a hole at approximately (3, 2) of the given diagram. A hole indicates that the numerator and denominator share a common factor at x = 3. However, the question is asking for the value of \(\frac{p(3)}{q(3)}\), which is the x-value of the hole. The denominator equals zero in this case, so \(\frac{p(3)}{q(3)}\) is undefined.

The3Mathketeers Aug 30, 2023

#2**0 **

**The Forum Fool is at it again, gracing us with his unparalleled ineptitude and absolute stupidity!**

GA

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Guest Aug 30, 2023

edited by
Guest
Aug 30, 2023

#4**0 **

**For the record: Post #2, signed by GA, is not by the real GA.**

**------------**

*The Forum Fool is at it again, gracing us with his unparalleled ineptitude and absolute stupidity!*

**The3Mathketeers is definitely not the forum’s fool. He’s a skilled mathematician with refined tutoring proficiency. He presents answers that are at the apparent level of the asker’s math-skill ability, without condescension, pedantry, or reductions in the unity of his presentation. The Forum’s asset value notably jumped, when he signed on.**

**For this question T3M presented an analysis and a learnable solution for an intentionally corrupted question, which is the typical fare of Maximum ...and several other members.**

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...and (not that you understand any of this, but) this irritates the crap out you, which is why you troll him.

GA

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GingerAle
Aug 30, 2023

#5**0 **

Really GA, does Web2.0 calc have a stock market which indicates how much homework cheaters value the site? This is probably the first user you have been able to talk about without using "imbecile", "moron", or any other insults in a long time. And no, The3Mathketeers solutions are utterly pendantic and contain unbearable ammounts of fluff, nor is he a "skilled mathematician" by any stretch. Perhaps you are so used to being condescending that this kind of prose is normal to you now.

Guest Aug 30, 2023

edited by
Guest
Aug 30, 2023