WPP #6: Unit I Concepts 3-5- Finding compound interest, continuously compounding interest, and investment application problems.

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SV #4: Unit I Concept 2- Graphing logarithmic functions and identifying all parts

In this video, I explained a problem about graphing logarithmic functions. I had to find the x-intercepts, y-intercepts, asymptote, domain, range, 4 key points on the graph, and then the final graph. The hardest part of this problem will have to be finding the y-intercept. I would say this was the trickets part because you have to remember to use the change of base formula. If you do not use it, then there is no way you can find the y-intercept. Another part that was pretty tricky would have to be x-intercept. I would say this was tricky because you have to remember to expotentiate both sides when trying to get rid of the log. Other than that, it was pretty easy. Thank you for watching!

SP #3: Unit I Concept 1- Graphing exponetial functions and identifying x-intercept, y-intercept, asymptotes, domain and range

In this student problem I made my own example of a graphing exponential equation. The first step in these types of problems is finding your a, h, b, and k. 'a' tells you if the graph is above or below the asymptote by the sign. If it is postive then it is above and if it is negative then it is below. B tells you what side, right or left, the graph is. If the absolute value of b is less then one (fraction) then it goes on the right side. If the absolute value of b is greater than 1 then it is on the left side of the asymptote. You find h by setting the exponent equal to zero and this shifts the graph left and right but for this example the key points do the shift. 'k' tells you if the asymptote moves up or down. If it is positive then it moves up units but if it is negative it moves down. You find the key points by adding four numbers to the 3rd key point. You find the asymptote by just looking at k because y=k. You find the x-intercepts by plugging in zero for y and for the y-intercepts you plug in 0 for x. The domain for these probelms will always be (-inf, inf) because an exponential graph has an asymptote of y=k, leading to no restrictions to the domain. The range depends on the asymptote. Lastly for the graph, you just plot in the key points and the intercepts.

The trickets part of these types of problems is probably finding the x-intercept. It was the trickets part for me because you need to make sure you divide by ln correctly and do all your intermediate steps correctly as well. Another tricky part of this problem will have to be the graphing. You need to make sure you do not cross the asymptote, plot each point you find correctly, and go in the right direction. 

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

These types of problems can be kind of tricky. One thing that is tricky about it is that you have to remember that extra clue you have which equals one. Another thing that can bE tricky about this concept is remembering to keep multiplying by 2,3,4, and so on if the numbers can not be matched up with the given clues. Always remember to break down the numbers to numbers that match up to the clues so you can make it into expansion form. Other than that, this concept about finding logs with given approximations was easy.

SV #2: Unit G Concepts 1-7 - Finding all parts and graphing a rational function

In this student video, I was to make up my own ration function and work out each thing. First I found all my factors of the equations and then worked my way into the full equation. Then I had to find my slant asymptotes by using long division. Once I completed long division, everything but my remainder was the equation of the slant asymptote. Next I found the vertical asymptotes by factorinf both the top and bottom of the ration function and canceling any common factors. Then i had to set the denominator equal to zero and solve. After i had to find the holes which were any crossed off commmon factors and set them equal to zero. To find the y-value of the hole, i had i needed to plug in the x value to the simplifeid equation. Then i found the domain which were the horizontal asymptotes and the holes. After i found the x-intercepts by setting the numinator equal to zero. Then there was no y-intercept for my problem. Lastly, i just graphed it by plugging in point and using the trace button.


 

The hardest part of this problem was graphing. The graphing is tough because you have the find the points yourself. Another reason why this is the toughest part is because you need to know the correct way the graphs are going.

SV #1: Unit F Concept 10- Finding all real and imaginary zeroes of a polynomial

In this student video, I was given a polynomails and I was suppose to find the complete factorization and all the zeroes. This problem is about getting a given polynomaial of 4th or 5th degree and finding all the zeroes. In this probelm we had to deal with real and complez First I had to find all the p's and q's. Then I did p/q to find the possible real/rational zeroes. After that I used Descartes Rule of Sign with f(x) and f(-x)to find out how many possible (+) real zeroes there was and how many possible (-) real zeroes there was. Then I used synthetic division to get my polynomail into a quadratic. Lastly I used the quadratic formaula to get the reamainig zeroes. The trickest part of this problem were the complex numbers. Using the quadratic can be hard if you mess up. If you mess up once, it can ruin your whole answer. With the complex numbers, you have to remember to simplify your answer all the way or it will be counted wrong. Other than that, Unit F Concept 10 is easy if you remember all the steps.

SP #2: Unit E Concept 7: Graphing polynomials and identifying all key parts

This student problem I made my own example of a polynomail that I graphed.I included the x-int which were (-2,0), (5,0) and (-3,0). I also included the y-int which was (0,-60). The zeroes were -2M2 (bounce), 5M1(through), and -3M1(through). The steps I needed to do to complete my problem was first make up my own factored equation. After I did that, I was able to get the whole eqaution by factoring them together. Then I was able to find the end behavior, the x-int with multiplicities, the y-int, and was able to graph it. Even though it was a huge y-int i made the y-axis going by tens and the x-axis by ones.

The trickest part of this problem is making sure you only cross the x-axis at the gates. If you do not graph it correctly you do not get it right. You can only go through the x-axis at the gates and makes sure it is with the right multplicity (through, bounce, and curve). Other than the graphing part everything else is pretty easy.