PatrickJMT Videos: Difference Quotients

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As we discussed in class (and as you saw in the homework!), the difference quotient of a function f(x) is

[f(x+h) – f(x)]/h

This is a concept that is at the heart of calculus (MAT1475 here at CityTech), which is why we’re studying it in precalculus. We haven’t yet discussed what the difference quotient represents. I’ll discuss it as some point, but the idea is basically contained in this graph:

Secant

(Hint: what’s the slope of the “secant line”?)

But for now, you should focus on calculating and simplifying the difference quotient of a given function. In addition to the examples we did in class and the examples in the book, here are a couple video examples by PatrickJMT:

Khan Academy Videos: Functions & Graphs

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I previously mentioned PatrickJMT‘s many many videos as a great resource to help you review and understand the material.

Another popular source of videos is the Khan Academy (created by a guy named Sal Khan). You can find videos organized into courses, not only on math but on many other academic subjects as well.

For example, he has sets of videos on Algebra, Algebra 2, and Precalculus. Here is a couple videos from the Algebra 2 sequences on Functions and Graphs which cover some of the topics we discussed from Chapter 2:


Evaluating with function notation

 


Introduction to piecewise functions: Sal explains what a piecewise function is, and finds the formula of a piecewise function given its graph:

Finally, if you’re interested, here is a TED talk Salman Khan gave 5 years ago, where he discusses how and why he created Khan Academy: “Let’s use video to reinvent education.”

PatrickJMT Videos: Solving Absolute Value Equations & Inequalities

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There are numerous online resources that you can use to help you understand the material. One collection of videos that I like is by a guy named “Patrick JMT“–as you can see, he’s posted on his website over 1000 short videos on a bunch of different math topics.  (You can also access them via his YouTube channel.)

You’ll have to look through his video titles to identify the ones relevant for our course–they’ll mostly be under the Algebra heading. For example, he has approximately 10 videos on solving absolute value equations and inequalities. Here is one that is a good summary of the techniques we discussed in class last week:

Welcome to MAT1375/D579: Precalculus

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Welcome to Math 1375, Precalculus! The course information sheet for our section can be found under the “Files” section of the course’s OpenLab profile.  (Note that there is a link to the Course Profile at the top left of this page.)

Read the course information sheet in detail, and hang on to it for the rest of the semester. It has important information, including my email address, office hours, grading policy, and some tips for succeeding in this course.

In fact, the tips are worth repeating here:

  • Attend class–take notes and ask questions!
  • Read the book–especially the examples!
  • Do the homework–ask about any exercises that you don’t understand completely!
  • Take advantage of additional resources–come to office hours, go to on-campus tutoring, take advantage of online tutorials!

Finally, please set up an OpenLab account and “join” the course profile to get announcements about updates to the course blog, discussion forums, uploaded files, etc.

(See https://openlab.citytech.cuny.edu/blog/help/openlab-help/ for instructions on how to create an OpenLab account. It is a very simple and quick procedure but you must have access to your CityTech email account.)