Tag Archives: patrickJMT

Video: Properties of Logarithms

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Here is a good video by PatrickJMT that reviews logarithms and their properties.  It covers:

  • the graph of a logarithmic function
  • the definition of logarithms, illustrated with some simple numerical examples (similar to exercise 13.4 on HW#8)
  • the properties of logarithms, and an example of using the properties to write a logarithmic expression in terms of elementary logarithms (similar to exercise 14. 2 and #2 on Quiz #3)
  • solving exponential equations using logarithms (similar to exercises 14.4 & 14.5)

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:

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: