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

Create your own Playlist on MentorMob!

SV#4: Unit I Concept 2- Graphing Logarithmic Functions

To view my video, please click here.

Make sure to pay special attention to the asymptotes and x/y intercepts. Since this is a logarithmic function, the asymptote will depend on h, not k like in exponential functions. So if you forget to take the opposite of h, then your graph will be wrong. For the x/y intercepts, you need to know how to exponentiate and solve logarithmic equations since they can get a little tricky or undefined.

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

Make sure to pay special attention to the asymptote and the x/y intercepts. The asymptote for exponential functions is from the k in the equation y= a x b^(x-h) + k, so you must remember to set it make it y=K not just k. When solving for the x or y intercepts, be sure to remember that is possible to end up with undefined answer; all that means is that there is no x/y intercept.

1. Find a, b, h, and k. Refer to y= a x b^(x-h) + k. *Remember that for h just put the opposite since it shows as x+1, it is actually -1 since 2 negatives make a positive.

2. Calculate the asymptote. Asymptote of exponential equations is y=k. So the asymptote would be y=  -2, not just -2 in its own. Then, draw the asymptote on the graph.

3. Solve for the x-intercept. Plug in 0 for y and solve. This will review your knowledge on solving exponential equations. Since you can't take the log or natural log of a negative number and zero, the answer will be undefined and no x-intercept. This is also logical because since the graph is below the asymptote of y=-2, then there in no way for it to cross it, let alone intersect the x axis.

4. Solve for y-intercept. Substitute x with 0 and solve. Plot the point on the graph.

5. Write domain in proper notation. Domain of an exponential function will always be (-infinity, infinity), which just means there are no x value restrictions.

6. Write the range in proper notation. This depends on the asymptote and graph. Since the graph is below the asymptote, it would be (-infinity, -2). 

7. Find 4 key points using a graphing calculator. Plot them on the graph.

8. Draw the graph by connecting the points and following the asymptote. 

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

To view my video, please click here.

This video will over how to find logs when given clues on how to find it. There are four clues that are given to you and two hidden clues that you can find using your knowledge of the proerties of logs. Using the clues and the power, quotient, anx product property, you will then be able to substitute the values/variables in and simplify to find what the log will equal.

Make sure to pay close attention to breaking down the numbers because some might already be a clue, but could still be broken down further. Also, ensure that you have the right signs when substituting in the clues: if it's in the numerator, then it will be positive because it multiplying; if it's in the denominator, then it will be negative because it is dividing.

SV#2: Unit G Concepts 1-7 - Finding all parts and graphing a rational function

To view my video, please click on the link here.

This video will go over rational functions and how to graph them. It will go also go over your knowledge on horizantal/slant/vertical asymptotes, holes, domain, and the x/y intercepts. Make sure you remember to put everything in its proper notation as well.

You need to make sure to pay close attention factoring and long division. This will ensure that your vertical asymptotes and holes are correct while also helping establish a boundary for your graph. Also, make sure that you have at least 3 points on each side of your asymptotes before making the graph.

SV#1: Unit F Concept 10 - Finding all real and imaginary zeroes of a polynomial

To view my video, please click on the link here.

This video will go over how you can find all the real and complex zeroes of a polynomial. It will draw upon your knowledge from Descarte's Rule of Signs, your p's/q's, synthetic division, and factoring.

You need to pay close attention to when you are factoring, so you can get all the right signs and numbers, when you are using synthetic division, and well basically everything. This is the type of problem that if you get 1 tiny detail wrong, the rest of your answers will be wrong as well.

SP#2: Unit E Concept 7 - Graphing a polynomial and identifying all key parts

Equation:

f(x)= x^4-5x^3+3x^2+9x

This problem is about is to see if you can use what you know about polynomials to make an accurate graph of it.  To solve it, you must need to know and understand how to factor a polynomial, the end behavior of certain polynomials, how to find the x-intercepts with multiplicities, the y-intercept, and how to graph the zeroes.

If you want to make your graph even more accurate, then you can find and use the extrema of the graph. In addition, be careful to make sure the end behavior is correct and the zeroes are correctly plotted. If a zero has a multiplicity of 1, then the graph goes through the point. If a zero has a multiplicity of 2, then the graph bounces off the point. Finally, if the zero has a multiplicity of 3, then the graph curves through the point. Make sure that all your zeroes match up to the highest degree (exponent).

1. Since we chose the zeroes(x-intercepts) first, multiply all the factors to get the equation.

2. Make note of the end behavior and how the graph will approach a zero (Thru, Bounce, Curve).

3. Find the y-intercept by plugging in 0 for x in the equation and plot it.

4. Draw the graph.

WPP#4: Unit E Concept 3 - Maximizing Area

Create your own Playlist on MentorMob!

WPP#3: Unit E Concept 2 - Path of Football (or other object)

Create your own Playlist on MentorMob!

SP#1: Unit E Concept 1 - Graphing a quadratic and identifying all key parts

Problem: 

F(x) = 6x² + 13x - 8

This problem is to see if you can identify the x-intercepts, y-intercepts, vertex(max/min), axis of quadratics and how to graph quadratics using the parent function. Already, just by looking at this problem, you already know that the graph opens up because a is positive.

To continue, you must remember how to complete the square, so you can convert it from standard form to the parent function equation, which would then make it easier for you to graph the function. After that, you can easily solve for x-intercepts, y-intercepts, vertex(max/min), and the axis of symmetry. Be careful with the x-intercepts because sometimes you might have imaginary numbers, but you wouldn't plot it on a graph because there is no axis for them.

Work:

Parent function equation:

y = 6(x + 13/12)^2 - 361/24

Vertex: (-13/12, -361/24) min.

Y-intercept: (0, -8)

X-intercept(s): 

(½, 0) and (-8/3, 0)

or

(0.5, 0) and (-2,67, 0)

After you finish the work, all you have to do is to plot the points on the graph and exploit symmetry to graph the quadratic (as shone below).