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.
Lesson NOtes (Notability – pdf):
This .pdf file contains most of the work from the videos in this lesson. It is provided for your reference.
Introduction to polynomial inequalities
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:
Rational inequalities
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!
Print this page
hello Prof. Reitz
It’s me Giovanni Feng, I would like to see the MAGIC video. I see a YouTube star in the making. Great Job on the videos professor!!!
Sincerely,
Giovanni
Thanks, Giovanni (*blush*) – I’ll try to make the Magic video this weekend, while I’m prepping for next week’s lectures.
I am just getting started – so please let me know if there are technical things I should be aware of (like if I’m not speaking clearly, or you can’t read my writing, or anything else that’s getting in the way…)
Hello prof.Reitz this is Mark, form lesson 12 I am having problem with Asymptotes.
Sure thing – I’m happy to help. You can either post your question here, in the comments, or you can click the “Ask for Help” button in WeBWorK to ask you question on the OpenLab’s Question-and-answer site. I’ll be notified either way, and will reply in the same place you ask.
-Prof. Reitz
Asymptotes Problem 9
Thanks! I took a look – can you tell me where you are stuck? For example, the first question asks about the domain – note that there will be a point not in the domain wherever a rational function has a vertical asymptote. The second question asks about the vertical asymptotes – where are they (looking at the graph)? Let me know your thinking, and I’ll do my best to give you some guidance…
Best,
Prof. Reitz
Before that I have problem with Problem 8 of Asymptotes
For problem 8, take a look at the roots. Are there any? (how do we find them?)
Hi professor , In example one, when you put the value of x=100, its equal to 126 not 134. Because you add the 4 instead of subtract.
For example one, why are we including the -1,4 in the answer? Can you please explain it?
please upload the magic video?
Hi professor , In example one, when you put the value of x=100, its equal to 126 not 134. Because you add the 4 instead of subtract.
For example one, why are we including the -1,4 in the answer? Can you please explain it?
please upload the magic video?
Hi Momna,
Thanks for the correction – great catch! I posted the Magic video yesterday – it’s here: https://openlab.citytech.cuny.edu/2020sprmat1375reitz/2020/03/21/lesson-12-followup-the-magic/
Let me know if you have more questions,
Prof. Reitz
Hello, Prof. Reitz
Im having a problem with asymptotes from lesson 12, ex. 9 looks confusion
Hi Eriseldo – Do you mean on the WeBWorK assignment “Rational Functions – Asymptotes”? (I think that was from the previous lesson, no worries either way). If so, let me know which part is giving you trouble. For example, for the domain, look for the vertical asymptotes – whatever the x-coordinates of them are, we need to exclude them from the domain (for example, if there was a single vertical asymptote x=1, then the domain would be (-inf,1)U(1,inf) ). Not sure if this helps -write back with more details and I’ll do my best to help out.
-Prof. Reitz