Sunday, October 27, 2013

SV #4: Unit I Concept 2: Graphing Logarithmic Equations

What is this problem about?

This problem goes over how to graph logarithmic equations and how to find key points such as x and y-intercepts. We also identify the asymptote, domain, and range. This type of graph is very different than exponential ones.

What does the viewer need to pay special attention to in order to understand?

Make sure you are correctly able to find your h because it will be crucial to finding your asymptote. In these types of graph we only care about h and k. Our asymptote equation will be x = h. P.S. h will be the opposite of what you see in the equation. Be sure to use the change of base formula when solving for your y-intercept and to correctly exponentiate for your x-intercept.

Happy solving!

Thursday, October 24, 2013

SP #3: Unit I Concept 1: Finding Parts & Graphing Exponential Functions

Let's start off by breaking off the steps to solve this problem!
So you first find the parts of the equation such as a, h, b, and k as in the first box. You then find your asymptote because your equation for this is y=k (remember YAK). You then proceed to find x and y intercepts (hint, you won't be able to find one of these *nudge nudge*) After this you can plot in the equation into your graphing calculator as is but remember to put parantheses around (x-1). Your domain and range should be especially easy to find, domain anyway. Your range depends on the location of the asymptote.

Ok so now:

What is this problem about?

This problem covers our favorite exponential functions and how to solve for their key parts. We use horizontal asymptotes for exponential graphs. So this is like intertwining two concepts (the graphing functions and exponential stuff)

What do you need to pay special attention to in order to understand? 

The exponentual YaK died! Don't forget that there will be no x-intercept because a is positive and it must go above the asymptote of y = 2. Range will depend on the location of the asymptote and direction the graph goes off in. Other than that don't forget to pay attention to what you input in your calculator! And do not make simple mistakes as I do and think h will be -1 instead of +1. OH and do not forget that when (1/2) is raised to -1, it will be become because you flip the fraction to get its reciprocal.

Tuesday, October 15, 2013

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

What is this problem about?

This problem is about finding logs when given approximations of course. The clues are given and the equation we are aiming to solve for. We need to break down the problem and expand our log in order to use the clues given to us. You then substitute in your clues. These problems demonstrate our ability to solve these without a calculator (for the most part because sometimes you do need help to break down the terms)

What does the viewer need to pay special attention to in order to understand?

Please be sure to remember log base 8 of 8 will equal to one. Do not forget how the quotient and power property will play a role in expansion and solving our log. Please please please take into careful consideration what these properties will do when you write out the expanded form. Also be sure to use the correct clues when you end up with your final form with your approximations!

Monday, October 7, 2013

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

What is this problem about?

This video covers rational functions. Horizontal asymptotes, slant asymptotes, vertical asymptotes, holes, domain, interval notation are included. These factors of the problem significantly contribute to our ability to graph the function. This problem however specifically does not deal with horizontal asymptotes. We focus on slant/vertical asymptotes and especially holes.

What does the viewer need to pay special attention to in order to understand? 

In order to better understand this problem, you must pay attention to every single detail. In order to find the equation for slant asympote, you need not go further than y = mx + b. Once you have the needed information, you can forget about the remainder since it is not necessary to us at the moment. Also remember even if it seems like the graph is touching the asympotote, it never, ever does.