This problem goes over a real life example of a problem from Unit I Concept 2. Concept 2 deals with an example that is a logarithmic graph and by identifying it as that, we know that x=k and there are no restrictions on the range. Because it is a logarithmic graph we have a new equation in which we use: log base b (x-h)+k. Also, for this type of graph it is only important that we understand that the domain is dependent upon the asymptote.
What does the viewer need to pay special attention to in order to understand the concept?
The viewer needs to make sure to pay attention on how to find the asymptote, instead of it being y=k it is now x=h for the asymptote so you need to make sure to know what h equals by looking back at the formula given. Yo must also play close attention to how you solve for both the x and y intercept because since we are now dealing with logs and natural log then we need to be aware that we know how to get rid of them, so that we can simplify further. Another important fact that we must remember and pay attention to is how to write the domain and range. For this type of logarithmic graph we should remmeber that there are no restrictions on range and for the domain will include the asymptote and an infinity sign.
This photo covers a real life problem of Unit I Concept 1 which deals with the graphing of exponential graphs. In this concept we deal with the equation y=a(b)^x-h+k and this equation is the basis of solving to find the rest of the elements in the problem. Once again, this concept deals with previous concepts that have come back to actually play another role in solving this type of problem such as knowing how to find the x and y intercepts involving logs and ln, how to find the domain and range of the equation, and how to label the numbers correctly with the right letter by remembering the equation used for this section. In this problem we also deal with figuring out the horizontal asymptote since it is an exponential graph and it has specific rules for the domain and range.
What must the reader pay close attention to in order not to make a mistake?
In order for the reader not to make a mistake when trying to graph an exponential graph is that you need to make sure that you memorize the equation y=a(b)^x-h +k. This is the basis of this problem because you need to know which numbers plug into the variables or else you may get the incorrect answer. You also need to make sure you know how to solve for the x intercept by setting y=0 and how to find the y intercept by setting x=0. Since this problem is an exponential graph you also must remember that these graphs have no restriction on domain but the range is restricted. The range depends on the asymptote and also on the number that a ends up being in your equation. The range is also depended on the variable a because if it is positive you have to make sure the range is (the #, inf.), and if (A) is negative it will be (-inf., #).
This video covers an example from Unit H Concept 7. Concept 7 is all about using what we have learned from previous concepts and applying them to another more complex problem, such as applying the knowledge we have of bringing one log together and then expanding it. We also use substitution in this concept when figuring out the expanded out log and plugging in the correct variable or number into the equation. In this lesson we also review how multiplication while solving logs, turns into addition. The main focus of this concept is to use the clues given to us to figure out the log given so that we can expand the log and substitute the values of the logs we expanded to form a new simplified equation.
What does the viewer need to pay special attention to in order to understand the concept?
The viewer needs to pay attention to each of the steps taken to ultimately figuring out the correct solution to the problem of finding logs with clues. Also, to be successful in solving this type of problem we need to remember to use two of the log properties to add onto our list even though they are not written on the paper. We need to be responsible enough to remember to the two properties that are log base b of b= 1 and log base b of 1=0. These two properties are two extra clues that can be used to helps us figure out what to substitute once expanding the logs. In order to also understand the concept it is critical that you remember that the logs with fractions may need to be multiplied by a number on top or bottom so that one of the clues given can show up. In your ultimate answer there should not be a log it should be the values given when substituted.
