WPP 6: Concepts 3-5: Compound Interest, Continuously Compounding Interest, and Investment Application Problems

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SV 4: Unit I Concept 2: Graphing Logarithmic Equations

The parts of the problem a student needs to pay attention to is how to plug in the equation into a calculator, since it is a little bit trickier than exponential equations. A student needs to know how to apply the change of base formula to input the equation into a calculator and determine other important points on the graph. Furthermore, a student needs to pay attention to the domain and range. There are no restrictions on the y-values, or the range, but there will be a restriction on the x-values, or the domain. The vertical asymptote permits any x-values that are less than or equal to negative 1.

SP 3: Unit I Concept 1: Graphing Exponential Functions

The viewer needs to pay special attention to how and why the graph does NOT have an x-intercept. Since taking the natural log of a negative number would be undefined, the graph therefore never crosses the x axis. Logically speaking, the viewer knows that the graph will be above the horizontal asymptote because "a" is positive. And since the graph will never cross over y=2, they can see that there will not be an x-intercept.

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

The trickiest concept to learn in this problem would be remembering to add in the extra clues to your list. Remember, logb(b)=1, so we can always use that when solving for the log. Another thing you have to watch out for is expanding the logs correctly. If the log has an exponent, you have to bring it to the front of the term and turn it into a coefficient, therefore getting rid of the exponent and being able to substitute the variables in correctly later on. This will ensure that your final answer with the variables is correct.

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

This problem is about graphing a rational function with a slant asymptote and hole. There are many aspects to this problem that a student needs to find before graphing the function itself. For example, there are slant and vertical asymptotes that restrict where the graph goes, which can be mentioned hand-in-hand with the holes of the graph. Also, there is the domain, y-intercept, and x-intercept to find in the rational function so you the specific points of the graph.

The things a student needs to look for in the problem is the possibility of a hole depending on the vertical asymptote. If you cancel something out when simplifying, you will have a hole and need to pay attention to that as well. The last thing that is notable in the problem are the windows: in this case, we will have to adjust them to see the graph accordingly. In addition, we will have to set our 10 by 10 graph to a different scale and probably count by twos if we want to be able to draw it there.