SP #4: Unit J Concept 5- Partial Fraction decomposition with distinct factors

In this student problem, I had to make up my own example of a partial fraction decomposition with distinct factor. I first had to compose my problem I made. Then i had to decompose it but now with replacing the top with letters according to the amount of facotrs i have on the bottom. Then i had to get a least common denominator for the three fractions by multiplying each part by what is missing. After i grouped them together and set it equal to the numerator that we first started with. Lastly we solve the equations by using matrices and the rref feature in our calculator and plus it back in. The most trickiest part about these types of problems is having so many variables. You can get confused with all of them so keep count on how many you are suppose to have. Another thing that was tricky is knowing how to use matrices because all these problems are related. One thing i found interesting was the rref feature gives us the answer so we know our work is correct. Other than that it was really simple. Thank you for watching! *Sorry i forgot to set it equal to the numinator in the 2nd picture :(

SV #5: Unit J Concepts 3-4- Solving three-variable systems with Guass-Jordan elimination/ matrices/ row-echlon form/ back-subsitution

In this video I explain DP problem number 3. I explained how to solve a three-variable system with Guassian Elimination and how to check your answer with the rref feature in your calculator. The trickest part in these types of matrix problems is being able to know what row to use. To make my life easier I just use the row on top so I won't get confused. It is really hard when you start mixing up the rows because you will get confused. Another thing that is difficult about these types of problems is making sure you know how to use your matrix feature. This feature is really helpful when checking your answers so if you do not know about it, you should. Other than that matrices are pretty simple if you do Mrs. Kirch's 4 step way of doing. One more thing, ALWAYS ALWAYS ALWAYS show your work. You need to show all your work so if you mess up, you will know where to go back and change something. Thank you for watching.

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.