WPP #6: Unit I Concept 3-5 - Compound Interest, Continuously Compounding Interest, and Investment Application

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SV #4: Unit I Concept 3-5 - Graphing Logarithmic Equations

In this video, the viewer needs to pay attention to how the logarithmic equation is not able to plugged into the graphing calculator because of its different numbered base (other than 10). In order for us to do so, we need to use the change of base formula- natural logs- which then gives us our graph. In finding the x-intercept, we must remember how to exponentiate and get rid of the logarithm. When finding the y-intercept it is important to know how to plug in the logarithm if the base is again not 10, which leads to using the change of base formula again. When finding the intercepts, if a number value of natural log is negative, the point is undefined. Because logarithmic equations are inverse to exponential equations, we know that the domain and range are flipped. The domain is restricted by the asymptote while the range has no restrictions.

SP #3: Unit I Concept 1 - Graphing Exponential Functions

The viewer needs to pay attention to "a", which determines whether the graph will be above the asymptote (positive "a") or below the asymptote (negative "a"). We also need to pay attention to solving for the x-intercept. If we get a negative number on one side, we cannot take the natural log of it, making it undefined. This is lead to NO x-intercept for this graph. Another concept to recognize for these problems are the range, which depend on the "a", whether it is above or below the asymptote, and the asymptote itself.

SV #3: Unit H Concept 7 - Finding Logs Given Approximation

This problem is about finding logs given approximations, which incorporated previous concepts learned, such as product, quotient, and power laws. It covers how to take our "clues" and multiply or divide them to equate them to our solution. We substitute the logs for the given values.

One thing to pay special attention to is recognizing that because there is a denominator, the log values will be subtracted. The viewer also needs attention themselves to expanding the clues using the properties of logs. If the log has an exponent, they need to use the power property, which then gives a coefficient to the log value. This means bringing the exponent to the front of the log. It is also important to recognize that you need to substitute in the values given after you have completely expanded your log.

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

The problem is about graphing a rational function. This video addresses vertical, horizontal, and slant asymptotes, and finds the holes and the x and y-intercepts of the function. Using past concepts (domain, long division, interval notation) will help us in graphing this function.

We need to pay special attention how to find the x and y-intercepts because it is crucial to remember to use the simplified equation, not the original rational function. Another concept we need to pay attention to finding the holes, plugging in the found x-value into the simplified equation to find the y-value of the hole. When plotting the hole, represent it as an open circle, which symbolizes that the graph does not go through this point. Lastly, through using the limit notation of the vertical asymptote, it gives you an idea of what the graph will look like.