Sunday, October 27, 2013
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.
In order to understand how to solve this problem, the viewer needs to pay special attention to the four parts of the exponential graph equation and how they affect the graph. Another thing to take note of is the fact that exponential graphs have an asymptote of y=k, which means that there are no restrictions on the domain (-inf. , + inf.). The viewer should also pay attention to how the range of the graph is written: from the lowest point to the highest point. Another thing to be aware of is the use of the 2nd TABLE function when obtaining the y-values of the key points.
Thursday, October 17, 2013
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.
Monday, October 7, 2013
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.