Rational Function Discussion by Donald Martocchio

Oliver Dunham

2025-06-25 15:14:26 UTC

From this meeting I learned about the proper way to do polynomial division with question 1f. I learned I had to include the 0x's as well to get my final answer.

2025-06-25 15:16:06 UTC

Quin

One thing I learned from the meeting was what I did incorrectly in problem 6. I was going to fast and forgot about the x in the denominator, and if I had been more careful while solving it, plugging 100000 into the function would have revealed the asymptote, which I originally got incorrect. My group helped me realize my mistake.

Summary of our meeting - Abby Caiola, Oliver Dunham, Quin Yannella

2025-06-25 15:18:20 UTC

We started off our meeting by answering the suggested opening questions to get to know each other a little bit. Then we went over all the questions and talked about the answers that we got for each . We spent a little extra time going over question 4 because we all struggled a little bit it. But in the end, we all figured it out and made sure there weren't any questions left.

Abby Caiola

2025-06-25 15:24:17 UTC

One thing I learned from this group meeting is that I move a little too fast sometimes when answering questions, and then I make small mistakes. I did this on question 1f because I made a mistake with the negative signs and got x^4+x^3+x^2+x+1, but during the meeting, I learned that the answer should have been x^4+x^3+x^2+x-1, and I went back and realized that I switched up the negative and positive signs.

Summary of our meeting - Isaac Graham, Michael Franco, Richard Fusco

2025-06-25 15:48:28 UTC

We spent the first few minutes of our meeting getting everyone connected to the call since there were some technical issues. After that, we began discussing the first few questions. We were generally in agreement on our answers for questions 1, 2a/b/c, and 3 but had a bit more trouble working through 4. Since 4 was a bit of a roadblock for us we skipped past it to go over 5 and 6 (both of which we didn't have any issues with) before coming back to the rest of 4 at the end of the meeting. We eventually managed to figure out the methodology for question 4 by slowly going through the teacher notes and following along with the solving process ourselves. By the end of the meeting we were all in agreement with our answers to the discussion questions.

Isaac Graham

2025-06-25 15:50:33 UTC

The most significant thing I learned from our group meeting was how to properly solve question 4 without any redundant intercepts which was something I hadn't previously figured out.

Michael Franco

2025-06-25 15:51:33 UTC

One thing I learned was how to process a question like number 4 and work through it. I saw the mistakes I made in the problem and worked through it with my group. I also learned some mistakes I made on polynomial division.

Richard Fusco

2025-06-25 15:51:49 UTC

The big thing that I learned from this meeting was how to properly work through question 4 on the discussion problem set. Rather than my strategy trying to work backwards on long division, I needed to start by solving for the remainder. I learned that I can just plug in 2 for x if I set the equation equal to zero since (x-2) is an x intercept. Then I can just solve for the numerator.

Amar SenGupta

2025-06-25 17:55:07 UTC

One thing I learned through the online discussion was how to solve problem 4. At first, I tried using desmos and found an equation that had the correct slant asymptote, but it had an additional zero. Previously, I submitted this, since I didn't know how else to solve it. Using both Mr. Martocchio's method of how to solve it, and advice from the group discussion, I realized that you have to start by using the remainder. You could use 2 for x (since its the intercept) if you set the equation to zero, and solve for the numerator. I never would have guessed that this method would work, since I wasn't super familiar with the relationship between remainders in the context of polynomials. This is one thing I learned through the discussion of the problem set.

Summary of meeting - Ethan Cohen, Amar SenGupta, Eliot de Haan

2025-06-25 17:55:21 UTC

We started by talking about our interests in math. Then we went through the questions one by one checking our answers against each others. Amar and Ethan helped me (Eliot) understand how slant asymptotes will effect the end behavior in Q. 1. We could all agree that question 4 was tricky and the way that we solved it resulted in an extra zero. We used Mr. Martoccio's notes to help us understand what we did wrong. We talked about how we remembered the quadratic formula for factoring an equation. We ended by talking about what we learned from this problem set and what we will submit to Canvas.

Ethan Cohen

2025-06-25 17:58:30 UTC

One thing I learned from this meeting was that I learned another method for Question 4. I got stuck on the part that required only 1 zero, and it was helpful to work through this issue and learn more about different ways to solve the problem, such as beginning with the remainder instead of the slant asymptote. We also discussed quartic asymptotes and how there can be more types of horizontal asymptotes(end behavior) beyond slant asymptotes, such as quartic and cubic.

Eliot de Haan

2025-06-25 17:58:35 UTC

I learned that slant asymptotes will affect the end behavior of a problem as it will always be approaching that line and it allowed me to revise my answers to Q. 1 e and f. My partners were extremely helpful in explaining this.

Dante Nejfelt

2025-06-25 18:17:24 UTC

One thing I learned about the meeting was how for some of the questions, like question 4, we all had differing ways of solving it and still ending up with the same/similar answers. Going over the answers we realized that we had the same answers for all the questions except the open ended ones.

Marina Yan

2025-06-25 18:20:50 UTC

I learned that I should be more confident in my answers, as when I originally did the worksheet, I thought some of my answers may have been wrong because they were unusual. For example, I didn't spot any holes in the first question, and I thought that was strange since if that was a question there should logically be holes in the equations. Turns out I was just overthinking it. I also learned that I was not the only one slightly confused by Mr. Martocchio's answer, as although we understood the explanation, we had trouble figuring out why our (we got the same solution) solution was incorrect, as it also approached 2x+1.

Alexavier Aviles

2025-06-26 01:22:10 UTC

I learned that it does not have to be always right, that its okay to make mistakes. I also learned about my classmates that they only enjoy certain type of math not all of it because it could get repetitive as well as my other peer found this work quite doable meanwhile for me was quite challenging since i have never learned this.

Summary of Asa, Anderson, Alex meeting.

2025-06-26 01:24:40 UTC

In summary we went through the questions from the to start double checking that we had matching or working answers. For questions 1 and 2 we all got the same answers but in questions 3 and 4 our answers varied a bit. In question 3 some of us had trouble with trying to get the denominators degree to match the numerator without adding asymptotes. In question 4 we had some very different equations. We all got the same answer in question 5. Question 6 was very straight forward and we all had similar explanations for what the horizontal asymptote showed. In we had revised answers and a better understanding of the solving process.

Anderson de Graaf

2025-06-26 01:31:10 UTC

Today in the meeting I learned that it is okay to use tools like Desmos a lot and that I wasn't the only person in my group who uses it to help with problems. But I also learned that while Desmos can be a very helpful tool you should always try your best before using it and not always having to rely on it. The meeting today really helped me learn this and see how other people similar to me also use Desmos and not just from my own perspective.

Asa Frost

2025-06-26 01:31:59 UTC

One thing that I learned in the meeting was that there were a lot different ways that people went about solving the same problems. In questions 3 and 4 we had all tried to solve them in slightly different way but in the end we all reached working answers. On question 4 the equations that we used to find the seconded factor varied but all fit the same function. It was cool to see the different ways that they solved them.

2025-06-26 01:38:57 UTC

Varun Venkataraman

Though we largely had the same answers, I still think I learned some things. For one there is more than one approach to solve a problem and end with the same answer. Second, I think I need to spend more time reviewing my answers, and I also need to get a little better at polynomial division.

Summary of Madison, Shiyan, and Varun

2025-06-26 01:44:03 UTC

We started by going question by question and comparing answers, which ultimately led to someone maybe having different answers than someone. If that happened, we would just find another way to all come on the same page. For example, if two people got the same answer and the other got a different answer, we would plug both into Desmos and see what the differences were and why the answer was right or wrong. All of us collectively struggled with number 4 and Varun gave an idea that Shiyan and I should plug into Desmos and that's how the idea sparked. Overall, we had mostly the same answers and were on the same page, though.

Shiyan Sun

2025-06-26 01:44:44 UTC

I learned that discussions really help you with your learning. When comparing answers, I can easily see what I did wrong and fix my answers and also, at the same time see what other people did to solve the problems and learn from them. In questions 4 and 5, I learned that my answers were wrong so I compared my answers with my group and found my mistake. For question 4, I put my answer and the answer my group got into Desmos to see what I did wrong and I managed to identify my mistake. We also used the same method to go through all the other questions. Additionally, I learned that you should at least try to do the problems even if you're not sure how to do them.

Lynx Herbig

2025-06-26 01:46:03 UTC

One thing I learned is that none of us got the same answer for the open ended questions, and it seemed like we really just all approached them in different ways. Though, some of our answers were not too different. I also came out feeling a bit more confident in my own answers for other questions, as my group mates got the same answers. This felt nice especially given the fact that I felt like I maybe had the wrong answer, like in question 5.

Andrés Solís

2025-06-26 01:59:37 UTC

In my meeting, I learned that not everyone got the same answers, which showed how we all had slightly different ways of thinking through the problems. Question number 4 was especially challenging, it made a lot of us stop and really think, and even then, we weren’t always sure we were right. But what stood out the most to me was that even when our answers were different, the steps and reasoning my group used were actually pretty similar. It made me realize that sometimes there’s more than one way to get to a solution, and talking it through with others really helps you understand the problem better.

Madison Williams

2025-06-26 02:17:16 UTC

I learned that different perspectives can help me learn a little better. We mostly had all the same answers but when we didn't, we had to find different solutions to get on the same page about things. We all collectively struggled on question number 4 so we went through and worked out how everyone did it and eventually got the same answer. I think having different ways to see the problem helps.

Anya Bhuyan

2025-06-26 19:09:01 UTC

From this meeting, I learned that for some problems me and my group members used different strategies even if we got the same answer. For the questions that we did get similar answers for, it was interesting to discuss our approaches because there might've been an approach that was more efficient than the others even if we all got the same result. For question 4, I heard about a lot of different methods for going about such a difficult question, and it was really helpful to hear other points of view even though we all got different answers. I liked hearing about how everyone interpreted certain problems since a lot of them weren't super straightforward and were more open-ended.

Summary of Anya, Andrés, Lynx Meeting

2025-06-26 19:14:59 UTC

It took us a few minutes to get everyone connected since we were having some issues with Pronto and decided to use Zoom instead. After that, we went through each individual problem and shared our answers as well as discussed the strategies we used and how we felt about each problem. We also talked about which problems took longer than others and why we thought that might be. We had the same/similar answers for all of the questions except for 4, which we all got totally different answers for and used different strategies as well. We spent a lot of time talking about 4 because we all agreed it was the most difficult problem, and we looked at Mr. Martocchio's answer together.