WPP#6: Unit I Concepts 3-5: Investment and Interest

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SV#4: Unit I Concept 2: Solving and Graphing Log Equations

~To watch my video, please click here~

For this video, you should make sure you understand how to find the h and k values. Knowing whether a log equation has a vertical or horizontal asymptote helps as well. Don't forget to try solving it yourself before watching the video!

SP#3: Unit I Concept 1: Solving an Exponential Equation

To solve this problem, you need to understand how to find the a, b, h, and k values. This is because they are key to finding the asymptote, domain, and range. You also need to pay attention to the coloured parts of the image, because chances they are important.

 

Step 1: Start with the equation (shown in the box titled 'equation') and determine if the graph lies below or above the asymptote. In this case, since the value of a is negative, the graph lies below the aymptote.
Step 2: Determine if the asymptote is vertical or horizontal by checking if it a log or exponential. In this case, the equation is an exponential one, and it's asymptote is equal to the k value. Therefore, the asymptote is 'y = -3'
Step 3: Solve for the x-intercept. Set y equal to 0 and add 3 to both sides. Then divide both sides by -2. At this point, we would normally take the log of both sides, but since you can't take the log or a negative (-3/2), there is no x-intercept.
Step 4: Solve for the y-intercept. Set x equal to 0 and simplify the exponent to 3. 1/2 to the power of 3 equals 1/8, and when you multiply that by -2 you get -2/8, or -1/4. Subtract 3 from -1/4 (I changed 3 to 12/4 to make it simpler) and you end up with -13/4. This means (0, -13/4) is your y-intercept- you can convert this to decimal form on your calculator to make it easier to graph.
Step 5: Determine the domain and range of the graph. Since this is an exponential equation, the domain is unrestricted. The range, however, depends on the asymptote. In this case, the range is -∞, -3.
Step 6: Graph the graph, haha that's an amusing phrase. Plug the equation into your graphing calculator and press the buttons labelled '2ND' and 'TABLE'. This will give you a table of all the points on the graph. Select a few, put them in your table, and plot them. Draw the aymptote, connect the dots, and voilà, you have solved this exponential equation.

SV#3: Unit H Concept 7: Treasure Hunt Logs

~*To watch my video, click here*~

This video shows how to solve a log using given clues. It also indirectly shows how to utilise the power, quotient, and product properties.

For this video, you should make sure you know and understand the properties of logs. Otherwise, some of the things I do in this video will not make sense. Also, it may be helpful for you to write the problem and steps down on a seperate piece of paper, as I have exceedingly bad handwriting and am entirely unapologetic for it.

SV#2: Unit G Concepts 1-7: Solving and Graphing a Rational Function

*To watch my video, please click the link here*

This video is about how to solve a rational function. It also shows how to graph the function.

For this video, you should make sure to write down all the pieces of the problem as I solve them. This is because I often clear the screen to give myself more room to work. If you don't write the needed parts down, you will probably find yourself replaying parts of the video more times than you'd like.

SV#1: Unit F Concept 10: Finding Real and Imaginary Zeroes

*~To view my video, please click on the link here~*

This problem is about how to find the real zeroes of a polynomial. It also shows how to find the imaginary zeroes of a polynomial.
For this video, you should make sure to pay close attention to the speaker. Do not be tempted to turn away from the screen, no matter how mind-numbingly boring the speaker is. You'll also want to follow along on a piece of paper.

SP#2: Unit E Concept 7: Zeroes and Multiplicity

This problem is about using randomly selected zeroes to create a polynomial. The zeroes should also be used to find the x-intercepts and the y-intercept. Finally, it should be possible to glean the end behavior and graph the equation as well.
For this problem, you should make sure you know how the multiplicity of a zero affects the graph of the equation. A multiplicity of one, for example, means that the graph will go through that point. Knowing the meanings of the multiplicity will make the graph more accurate.