WPP #6: Unit I Concepts 3-5: Compound Interest, Continually Compounding Interest, and Interest Application

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SV #4: Unit I Concept 2: Graphing logarithmic functions and identifying x- intercepts, y - intercepts, asymptote, domain, range (4 points on graph minimum)

In order to understand the problem, the viewer must be attentive to several elements. Firstly, it is important to identify your h and k accurately, otherwise many parts of your problem (if not the whole problem) will be incorrect. Also, one must be meticulous in their work for the intercepts. Lastly and obviously, one must make sure to plug in the equation to their calculator, correctly using the change of base.

SP #3: Unit I Concept 1: Graphing exponential functions and identifying x- intercept, y- intercept, asymptotes, domain, range (4 points on graph minimum)

Hey this is Michael C. from Period 5. In this picture we will be graphing an exponential equation and identifying key parts. The equation we will be using is y = 5(1/2)^(x - 1) + 1. First you will identify the a, the b, the h, and the k. The next logical thing to do is find the equation for the asymptote which should be y = k. Then You find the x- intercept by setting y to zero (it should be undefined for this problem since the asymptote is y = 1 and the graph must be above it so the graph will never come into contact with the x- axis.) and the y- intercept by setting x to zero. Domain for these problems will always be all real numbers since the graph goes infinitely to the left and right. Range will depend on the asymptote and wheter the graph is above or below it, and it's above in this problem. Next you want to use some key points and the h should be your 3rd point. Plug the equation into the calculator and use the table to get the points and plot the points. You know that the graph should be heading toward the asymptote on the right side since the absolute value of b is less than 1. And that is all.

When solving this problem one must pay attention to a few things. Firstly you must be precise in identifying a- k. Second, you must make note that the x- intercept is undefined because of the asymptote. Also, you must remember that there are no restrictions for the domain and the range depends on the asymptote.

SV #3 Unit H Concept 7: Finding logs using approximations (treasure hunt)

In order to fully understand the problem the viewer must pay special attention to a few things. One, the viewer needs to pay attention to the clues. Two, the viewer needs to be sure that they have broken apart the problem correctly to get the right clues to use. Then, the viewer must expand the log correctly, so when it's time to substitute the variables in, the problem will be correct.

SV 2: Unit G Concepts 1-7: Finding asymptotes and holes and graphing rational functions.

1). This problem is about finding asymptotes and holes of graphs of rational functions. We will be using the function x(x +2)(x - 1)/ (x + 2) (x +1). This video will go over how to find the slant asymptote, the vertical asymptote, and the holes of this function. We will also be finding the domain, the x- intercepts, the y - intercept, and the actual graph of the function. What does the fox say?

2). One must pay attention to several things while doing this problem. Firstly, one must be sure to factor the function correctly and be careful when doing long division for the slant asymptote. Additionally, it is important to remember to put parentheses in the correct places when plugging the function into a graphing calculator. If the parentheses are left out, the graph will be wrong in the calculator.

SV #1: Unit F Concept 10: Given polynomial of 4th or 5th degree, find all zeroes (real and complex)

1). This is  a problem about finding all zeroes of a quartic polynomial. The polynomial we will be using is 25x^4 - 80x^3 + 58x^2 - 3. We will be combining all of concepts 3-9 in this problem. Also, we will be doing something different than what we did in those concepts because we will also be finding all irrational/ imaginary zeroes as well as the rational ones.

2). The viewer must pay attention to several things. One major thing the viewer needs to pay attention to is that the polynomial we are using doesn't have a term for x to the first degree. Thus, the viewer mustn't forget to put in a placeholder when doing synthetic division otherwise the problem can go wrong. Also, the viewer must pay attention to how to put the non factorable quadratic into factor form once the irrational zeroes are found.

SP #2: Unite E Concept 7: Graphing polynomials, including: x -int, y-int, zeroes (with multiplicities), end behavior. All polynomials will be factorable.

(1) This problem will go over how to graph a polynomial and find the characteristics stated in the above title. In this particular problem, we will be using the quartic polynomial  x^4 - 4x^3 - 12x^2. In order to complete the problem, we will be going through a number of steps, including factoring the polynomial, finding end behavior, solving for the x and y intercepts, calculating extrema and intervals of increase/decrease, and of course graphing.

(2)The reader must pay attention to detail for a little mistake could ruin the entire graph. Also, one thing the reader must be attentive to is the set window when plugging the polynomial into a graphing calculator to graph. This is because the problem results in large numbers and as a result the graph does not fit into the standard zoom.

• First we factor out an x squared and factor the rest of the equation from there. The resulting factored equation is in the 2nd box of the picture above.
• The end behavior part is as it is because the highest degree is 4 which is even, and the leading coefficient is positive, so the graph is an even positive meaning both ends point up.
• To get the x- intercepts, you take each individual part with an 'x' from the factored equation and set them equal to zero. The zero of (0,0) is repeated because of the x squared so it has a multiplicity of 2.
• For the y- intercept you just plug in zero into x from the original equation.
• Maximums and minimums could be found using 2nd cal on your calculator and following the instructions. Next, find the intervals using the extrema.
• Plot the zeroes and extrema on a graph. Next, figure out how the graph goes through each zero. To do this, refer to the multiplicities. A multiplicity of 1 means the graph goes straight through the zero, whereas a multiplicity of 2 means the graph bounces off the zero. Since the end behavior is even positive, both ends of the graph point up. Now draw the graph and you will be finished.