WPP #6: Unit I Concept 3-5: Compound Interest, Continuously Compounding Interest, and Investment Application

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This Word Problem Playlist goes over compound interest and how to find the interest or time given certain information. There are some tricky part in trying to solve the problem, such as remembering to keep the quotient a fraction when dividing the total resulting money by the principal. When completing this, remember to get enough numbers so you can get to a rate that has a percent that includes the hundredths as well. It is also significant to remember that the needs to be rounded to be nearest month using proportion of x/12. Lastly, the most important part is to remember all the formulas that accompany each part of the problems, so you do not get confused. Good luck! 

SV #4: Unit I Concept 2: Graphing Logarithmic Functions

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This video goes over logarithmic functions and also includes the parts that help find the graph to it. There are many key factors that you must pay attention to because this time around there's a log involved. Given this information, you know that for the x-intercept, we have to exponentiate in order to get rid of the log. Also, for the y-intercept, you must remember to change the base in order to figure our the ordered pairs. Also, in order to graph the equation, you need key points of significance. However, in order to get thoe points, you first need to plug it into your calculator the way I described in the video, so please make sure to do this before continuing. Lastly, as a clarification, the graphing calculator will not entirely graph the equation correctly, so the part left of -5, which is the asymptote, will be blank because of that same reason. Don't worry though, you do not need to graph that section. Other than that, thank you for watching :D

SP# 3: Unit I Concept 1- Graphing the Exponential Function

          This Student Problem goes over functions and explains how to graph one. As you can see, the function is composed of an exponent and is in the form of a parent graph. Using the values, key points, asymptotes, x-intercepts, y-intercepts, domain, range, and range, the image provided showcases a correct graph for the function. You will find that my ordered pair (2,-17) is off the graph, so it is place at the bottom of the graph just as a guide to help draw the graph.
          In order to successfully solve this function, remember that there are some key factors that will determine the graph, such as the x-intercept. To find the x-intercept, start by substituting a 0 for the y-value and continue the process of solving the problem. After some addition (+5 to both sides) and diving (-3 to both sides), you will notice that you get -5/3. Move the exponent (x-1) to make it a coefficient and you will go over natural logs to get rid of the 4. However, the problem is that you cannot divide the logs, as LN -5/3 is negative and one cannot divide negative logs; it would be undefined, so there is no x-intercept. Remember that for the y-intercept, you have to solve the 4^-1 properly by finding its reciprocal of (1/4). For guidance, the "a" value will help you determine whether the asymptote is below or above, but in this case, it's above. For the key points, it's helpful to use ordered pairs that are not all so close together, so you can get a better view of your graph.

SV#3: Unit H Concept 7- Finding logs given approximations

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          This is problem goes over how to find logs based on approximations. Before you start remember to add logbB=1 and logb1=0 to your given clues in case you need them. For this particular problem, we will only be using the property that equals 1. Another important thing that you must remember is the difference between product and quotient logs.  Also, just to make this problem easier, divide the log your are looking for  by the given clues so you won't have to take much time trying to figure out which factors will work for the problem Logs that have addition in between them are product (vice versa) and those that have a subtraction sign are quotient (vice versa). When your expanding, you should have one log for each number so you can then substitute in the values or letters that were given at first. I did not mention this is in the video, but implied that each number has to have a log, so I hope that makes sense now,if it didn't before. Thank you for watching! 

Again, I am sorry for the mistake. Basically the only difference is that all the factors on the denominator will have subtraction signs as it is a quotient considering that is underneath the numerator. 

SV#2: Unit G Concepts 1-7- Finding All Parts and Graphing a Rational Function

SV #2: Unit G Concept: 1-7 Rational Functions

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          This video goes over rational functions and as well includes the slant asymptote, vertical asymptote, holes, domain, intervals, and explains how to graph it. This functions does not include a horizontal asymptote because its leading degree on the numerator is bigger than the leading degree on the denominator. Therefore, this graph has a slant asymptote with one hole and two x-intercepts. Along with that, this video goes over notations, equations, and ordered pairs.
          In order to understand this problem better, you must note that the slant asymptote does not require you to continue solving past the needed y=mx+b equation. Along with that, because you have the same factors on the numerator as well as the denominator, the graph is going to have a hole. The graph will then skip the ordered pair as it is a hole. Lastly, it is very important to remember that the graph does not touch the asymptote even though is might seem as it does.

****Correction:
I'm sorry for the mistakes, but here is a correct version of the graph. For the holes, the canceled factor, which leads to the equation x=-3, is the x-intercept for the ordered pair. You just have to plug in the x-value in the equation as shown in order to get the y-value of -3/4. This means that the hole on the graph changes, but you still have to skip it as it does not exist on the graph when you trace it (please see the graph from the picture). As for the y-intercept, you have simply plug in 0 for the x-values in order to find the ordered pair of (0,0). Other than that, the rest is correct.