SV #3: Unit I Concept 2 (graphing and identifying the components of a logarithmic equations)

The trickiest part of graphing a logarithmic equation is remembering how to find the components of these equations. For a logarithmic the asymptote is always x = h, which in this case is -3. The domain is always dependent on the asymptote. Another tricky part is plugging in the equation correctly into my calculator because we have to use the change of base formula.

ps. The end of the video showing the graph and the plotted points were cut off. The ordered pairs I used were: (-2, -2), (1, -1), (3, -.708), (5, -.5). The graph goes near the asymptote, almost touching it but never crossing it.

SP# 3: Unit I Concept 1 (graphing exponential functions)

 

The trickiest part to graphing the equation was getting my intercepts. When we get our asymptote, it is better to then figure out whether we have x-intercepts which could be really confusing. We will only have x-intercepts if it crosses the x axis either below or above the asymptote (depending on the sign of a).When finding an x-intercept, we usually will have to divide logs so remembering to use parenthesis is critical.

SV# 3: Unit H Concept 7 (finding logs using approximations)

In this video the trickiest part is to realize that any log can be broken up in different ways. A log can be expanded in several different ways correctly. Also, it is easy to forget that regardless of the amount of clue already given to us we always have two "hidden" clues. In this case, ours were log base 8 of 8 which if we were refer back to concept eight, we know that if the base and the value are the same number, it simplifies to one. The second given clue is log 8 of 1 equalling zero because any log base of 1 equals zero. Always remember that the numbers MUST be broken down using only using the clues to then expand the log completely.

SV #2: Unit G Concepts 1-7 (graphing rational polynomials)

 

In this video we discuss how to get all needed plots in order to graph a rational function. First, we need a rational function equation and a rational function equation must be a fraction with both the numerator and the denominator being polynomials. Then we decide whether our equation has a horizontal asymptote or a slant because a function can NEVER have both. If we refer to our in-class-chant we know that if the degree on Top is One bigger than the degree on bottom, we have a slant! And to get that slant equation, we need to use long division but ignore the reminder. Next is to find vertical asymptotes and holes. If after factoring both the top and the bottom we notice that a set in parenthesis can be canceled from top and bottom, then that becomes our hole(s) and we can now use the "simple" equation to set the denominator to zero and get our vertical asymptotes. Rememeber, Domain is always the vertical asymptotes and the holes (only x-intercept). To get the x and y intercepts, the simple equation must always be used. For x, set the numerator equal to zero; for the y, plug in 0 for every x value. After getting all of that, we must find three different plots for each side and only then may we solve. Check your graphing to get your plot ordered pairs.

 

The trickiest part in solving this equation was actually figuring out how to graph it. When plugging into my graphing calculator, it wouldn't give me an accurate graph and I didn't know why until I remembered that *parenthesis must always be put seperately around both the numerator and the denominator. After that it was then easy to solve.

SV#1: Unit F Concept 10 (finding all zeroes of polynomials)

In this Student Video, I cover the process of how to find all zeroes of 4th/5th degree polynomials. There were four main things asked to look for: one, find possible positive and negative zeroes; two, find rational zeroes for each function; three, find all zeroes (most crucial step); and four, writing the complete factorization of the zeroes. When finding all of these things, it is helpful to write everything down. I will go over each step as thouroughly as I can in the video.

https://www.youtube.com/watch?v=mCJU0TFFIrQ

While watching this video, Isuggest to pay attention to the side notes which tell what are steps will bne. This will minimize confusion and could clarify any question about any section of the mathematical process. I do try to speak slowly to keep from confusing the viewer but if you feel like you understand, feel free to skip any section of my explanation. Thank you for watching!