SV#5: Unit J Concepts 3-4: Solving Three-Variable Systems with Gaussian Elimination & Solving Non-Square Systems

     In order to understand how to solve this problem, the viewer must pay special attention to the four steps of  Gaussian elimination. They are important to know, because they avoid the possibility of redundant or unnecessary work. Another thing that the viewer should take note of are the steps of checking answers using the Reduced-Row Echelon Form (RREF) feature on a graphing calculator.

SV#4: Unit I Concept 2: Graphing Logarithmic Functions & Indentifying Key Parts

     In order to understand how to solve the problem, the viewer must pay special attention to the sentence: "The LOG's Xylophone was Happy and Rich." This means that the graph of a logarithmic function has an asymptote of x=h, and that there are no restrictions on its range. Another thing that the viewer should take note of is the use of the Change of Base Formula throughout the problem. This is crucial because it enables one to correctly input logarithmic functions into a graphing calculator.

SV#3: Unit H Concept 7: Finding Logs Given Approximations

                                     
     In order to understand how to solve this problem, the viewer needs to pay special attention to the "clues" that are given. They are important because they guide you when expanding your expression. They viewer should also focus on the properties of logs, because they help us determine our two "hidden clues". One more thing that the viewer should pay attention to is that when factoring the parts of the initial log, you can stop once you have found your clues.

SV#2: Unit G Concepts 1-7: Graphing Rational Functions

                                                                                                                    
      This problem is about how to graph rational functions and all of their parts. In this problem, we encounter a rational function with a slant asymptote instead of a horizontal asymptote. After finding the asymptote and its equation using long division, we then solve for the vertical asymptote, its equation, and limit notation. In this problem we obtain one hole. Once we have found the domain, x-intercepts and y-intercept, we the graph the asymptotes and all the other components of the rational function on a coordinate plane.            

     In order to understand the problem, the viewer should pay special attention to the process of factoring trinomials and other polynomials. In addition, they should focus on how to write the limit notation of the vertical asymptote and the domain of the graph. The viewer would also greatly benefit from paying attention to the use of the factored rational function throughout the problem.

SV#1: Unit F Concept 10: How to Find All Real & Complex Zeroes FromPolynomials of 4th or 5th Degree

     This problem is about how to find all zeroes (both real and complex) when given a polynomial of the 4th or 5th degree. In this problem, one must find the p's and the q's of the polynomial and and then utilize Descartes Rule of Signs. Afterwards, synthetic division is applied to determine any or all real zeroes, and to reduce the polynomial to a quadratic. In order to find the complex zeroes, one can either factor or plug in the values of the quadratic into the Quadratic Formula.

     In order to understand how to solve such a problem, the viewer needs to pay attention to the steps taken to find all of the possible real zeroes. This is important because it enables them to narrow down from literally an infinite amount of possibilities. Another thing the viewer needs to pay attention to is how to rewrite the complex zeroes after using the Quadratic Formula.