A City Tech OpenLab Course Site
Hi everyone,
In one of the examples during Lesson 12 last week (it was Example 2), there was a place where we needed to solve the following equation:
$x^4-5x^3-x^2+5x=0$
In the lesson, I used magic to find the roots — in this video, I’ll actually go through the steps:
Hi everyone! This is the first of our distance-learning lessons. Read through the material below, watch the videos, and send me your questions.
Lesson 12: Polynomial and Rational Inequalities
Lesson Date: Thursday, March 19th.
Topic: This lesson covers Chapter 12 in the book, Polynomial and Rational Inequalities.
WeBWorK: There are two WeBWorK assignments on today’s material, due next Thursday 3/26:
Polynomials - Inequalities, andRational Functions - Inequalities.
This .pdf file contains most of the work from the videos in this lesson. It is provided for your reference.
Definition. A polynomial inequality is an inequality (which means it uses one of these: $<,\leq,>,\geq$ instead of an equals sign) with a polynomial on each side
Example 1: $x^2-3x-4\geq 0$
We’re interested in solving these inequalities, which means answering the question: “For which real numbers x is the inequality true?”
Now let’s look at the same example, and see how to solve it without looking at the graph:
Example 2: Solve $x^{4}-x^{2}>5\left(x^{3}-x\right)$
Example 2, concluded:
What happens if we allow rational functions instead of just polynomials?
Example 3: Solve $\frac{x^{2}-5 x+6}{x^{2}-5 x} \geq 0$
Good job! You are now ready to practice on your own. Take a look at the WeBWorK assignment, and don’t forget to use the “Ask for Help” button if you get stuck.
Here are more video resources if you’d like to see additional examples.
ASSIGNMENT: Watch videos, try webwork. Ask questions in comments below, or using the “Ask for Help” button in WeBWorK. Good luck, and stay safe!
Hi everyone,
These are challenging times, filled with unknowns – I know everyone’s lives have been turned upside down. I, and the rest of the faculty at CUNY, are pushing ourselves to learn new technology tools and to think creatively about how we will continue your college education from a distance. I wanted to post a brief update today, to let you know more details about how our class will be run going forward, and to give you a chance to ask questions (feel free to comment on this post).
What’s going on in terms of our class right now? Right now, all of CUNY is in a “recess period” until tomorrow (Wednesday 3/18) – this means that our classes are on pause. On Thursday 3/19 we will officially resume class, but through distance-learning only (we will not meet face-to-face).
When will we meet again face-to-face? CUNY has announced that classes will not meet face-to-face for the rest of the semester.
How will we hold class if we are not meeting face-to-face? Great question. Over the next few weeks we may try a few different things, but this Thursday our class will work as follows: I will post a lesson on the OpenLab, including some things to read and some videos to watch. I will also assign WeBWorK based on this material, and provide some different methods for you to ask me questions.
How will exams be handled? I still don’t have an answer to this, although we are considering a variety of options. Our next exam (originally scheduled for this Thursday) is cancelled for now – it may be rescheduled, or replaced with quizzes, or some other solution.
What if I have questions? For questions on WeBWorK, I encourage you to use the “Ask for Help” button at the bottom of every problem. This will take you to the WeBWorK Question and Answer site on the OpenLab, and (once logged into the OpenLab) will allow you to ask a question about that specific problem, and view questions and answers that others have asked about that problem. NOTE: Your question will be anonymous, so no-one (except me) will know that you wrote it.
For general questions, feel free to post on this OpenLab page (either comment, or create a new post), or send me an email: jreitz (at) citytech.cuny.edu.
What if I need more practice? I have enabled the “Show Me Another” feature in WeBWorK (the Show Me Another button appears at the bottom of the problem, next to “Submit Answers”). This gives you a chance to work on a similar problem, without affecting your WeBWorK score. You can check your answers and look at hints.
That’s it for now – check your email and the OpenLab regularly for updates. Take care of yourselves and your loved ones.
Best regards,
Prof. Reitz
Hi everyone,
As you may have heard, CUNY is taking a number of steps to help prevent the spread of Covid-19. These include:
Keep your eyes on the OpenLab for future announcements. Keep studying and doing your WeBWorK. Stay calm. Stay alert. Wash your hands often. Take care of yourself and your loved ones. Past experience shows that troubled times bring out the best in New Yorkers, and I believe this is no exception.
As always, don’t hesitate to contact me (by email, or by leaving a comment below) if you have questions or concerns.
Best regards,
Prof. Reitz
Hi everyone,
I know this is a difficult time and it is hard to know how worried to be, or what is the right action to take, in the face of the Covid-19 coronavirus. I ask for your patience and cooperation as we navigate this public health challenge together. I’m here to pass along some information from the college, and to ask for your input.
From the Provost: At this point–although it could change quickly–the college is open, and our general message is that unless a faculty member or a student has tested positive for the virus or has good reason to believe they may have been exposed, they should come to class.
In order to be prepared in the event that the college does cancel class meetings, I’m asking you all to complete the brief survey below about your access to technology and ability to participate in various ways from off-campus.
If you have concerns or questions, don’t hesitate to email me or speak to me directly.
Any updates that I receive will be posted to the OpenLab.
Thanks,
Prof. Reitz
In the event that you are not able to attend class, or that class meetings are cancelled, please describe your ability to connect to classroom resources from home/off campus.
The review sheet can be found here. If you have questions or notice any errors, please let me know by email or in class.
Regards,
Prof. Reitz
Hi everyone,
Exam #1 has been graded and will be returned Thursday (tomorrow). If you are a member of this class on the OpenLab, you can view your grade at:
Dashboard/OpenLab GradeBook
(the Dashboard is accessible by clicking the name of the course in the black bar at the very top of this page, provided you are logged in to the OpenLab and already a member of the course).
Best regards,
Prof. Reitz
Hi everyone,
Due to circumstances beyond my control, I have not been able to finish grading the first exam. Please accept my sincere apologies – I do not take this laps in responsibility lightly. Your exam will be returned on Thursday this week.
Regards and regrets,
Prof. Reitz
Hi everyone,
I made two corrections to the Exam #1 Review Answer Key, as follows:
Problem 8c, the correct answer is: $(f\circ g)(x) = \sqrt{2x-16}$, domain $D_{f\circ g} = [8,\inf)$.
Problem 9c, the correct answer is: $h^{-1}(x)=\frac{1-x}{2x}$.
If you see any additional errors, please let me know!
Best,
Prof. Reitz
Hi everyone,
My apologies, I must cancel my office hours this week on Tuesday 2/20. I will be available on Thursday as usual, and by email as well.
Best,
Prof. Reitz
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