WPP #6: Unit I Concept 3-5: Interest and compounding

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SV #4: Unit I Concept 2: graphing logarithmic equations

               This video will show you how to graph logarithmic equations using the needed parts. It is similar to solving for exponential equations in that you need to find the same parts like h, k values, key points, asymptote, y and x intercept, domain and range. However, you do not need to find a, b values and the asymptote is vertical so x=h. Furthermore, you solve for the x and y values differently than in exponential equations. Finally, the domain is not all real numbers, instead it has an end point while the range is all real numbers (negative infinity, positive infinity).
            Remember that the logarithmic equation is the inverse of the exponential equation. This will help you remember what are the differences between them and how to find the different parts.

SP #3: Graph the exponential equation, filling out all needed parts

                             This problem shows how to graph exponential equation. It has the key parts we are already familiar with which are the a, b, and k values. The a value in this type of equation shows us at first sight whether the graph will be above or below the asymptote based on whether the value is positive or negative, and k value is the the y=k asymptote. In this equation k=1 so the asymptote is y=1 and since the the a value is positive the graph will be above this asymptote. You can also find other key parts to be able to graph this equation. These parts include: key points (you get from the calculator easily), the x and y intercepts, and the domain and range. Remember that the domain in an exponential equation will always be all real numbers while the range will be either from negative infinity to the asymptote or from the asymptote to positive infinity. In this case it is from 1 to positive infinity.
                            You must pay close attention to whether the graph will have or not have an x-intercept. You know whether the graph will have a x-intercept by knowing that if the equation leads you to getting the log (or natural log/common log in your calculator) of a negative then you cannot solve this equation and therefore there is no x-intercept. A short cut to knowing there is not or there is an x-intercept is by looking at the a and k values of the exponential equation. if they are both positives or both negatives values then the equation will not have an x-intercept like in this example. But if the a and k values differ in that one is negative and the other is positive then there will be an x-intercept.

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

                                    This video shows you how to find a log with given clues, so it is like a treasure hunt. You use the given clues to add them or subtract them to one another using the product and quotient laws as well as the exponential law. You must also be sure to know the log property that shows that a log base (b) and the number (b) will equal one and use this clue besides the other clues given to solve the treasure hunt. This could be similar to finding the factors of your "treasure"(the log you want to find) but instead of coming up with random factors you use the ones given in the clues.
                                     Remember that when you use a clue more than once you use the exponent law to put the exponent number in front of the clue you used more than once when writing out your solution. Also, remember how to use the property log shown above properly. To illustrate, when you have log base (7) 7 you know that equals 1. However when you are solving the log you need to find you use the number 7 one of the possible factors, you do not use the number one.

SV #2: Unit G Concept 1-7: Graphing polynomials and their asymptotes

                        In this video I am explaining how to graph the polynomials with their asymptotes. The asymptotes are like boundaries that the graphs cannot touch except maybe sometimes for the horizontal and slant asymptotes but never for the vertical asymptotes. I show how to find the equation and points for each of these asymptotes. Furthermore, I show how to find holes in the graph. Plus, the domain, y and x intercepts and graphing more points using the calculator.

                       One thing you must special attention to is that when you have a hole you find the x intercepts and y intercept by using the simplified equation, not the original equation.

SV #1: Unit F Concept 10: Given Polynomial of 4th or 5th Degree Find ALL Zeroes, including real and complex.

                                 In this video you will learn Unit F Concept 10, which is similar to Unit F Concept 6. The difference is that you will end up with irrational zeroes at the end instead of just rational numbers. You will follow the same steps as in the Unit F Concept 6 until the end when you end up with irrational zeroes. You will learn how you found irrational zeroes in the first place, and you will learn how to put them into factor form, in factorization.
                                 One thing you need to pay close attention to is that when you write out the factors you must have a number of "x's" in the factorization equal to the degree of the equation. This means that if the equation is up to the fourth degree then you must have four "x's" in your factorization. You cannot leave the irrational zeroes without the x and count them as factors. They are not factors unless you use the proper way to turn them into factors with the variable x.

SP #2: Unit E Concept 7

                  In this Student Problem we are first reviewing how to create a polynomial expression starting with the zeroes and their multiplicity. This is labeled 1 with a circle around it in the picture above. Then, the following step are numbered as well up until six. All the steps shown are taken to learn how to use information known to graph a polynomial. This information includes: how to find factors based on zeroes, how to multiply factors, how to interpret end behavior, how to solve for your y-intercept, and finally how to use the multiplicity number to know whether the line of a graph goes through, bounces, or curves.
                  In order to complete this student problem correctly you must remember that the zeroes are opposite of the factors so it will always be (x minus "zero"). Another key thing you must remember is how to know whether a line goes through, bounces, or curves using the multiplicity number. Mrs. Kirch's catchy tune of "1,2,3, TBC" is a good way to remember. If the multiplicity is 1, then the line goes Through, if it is 2 then the line Bounces, and if it is 3 the line Curves.