Sit down and Shut UP

Dr. Max B Sherman
Pre-Calculus
Harvard University
4/11/2020

Hello class, I'll be your professor for this semester. Let's get a few things out of the way first:
1) Under no circumstances will I allow any technology in the classroom. This will be the only 90 minutes of your day that your not connected, so enjoy it instead of dreading it.
2) Even if you don't plan to become a Mathematican like me, pre-calculus will help you throughout your miserable lives, so pay attention
3) Your grade is not based on your test scores, but on your active particpation and willingness to learn in class. The grades are only there because Harvard requires them.

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Domain & Range

Today we will be covering the domain and range of functions and graphs. The first thing to learn is the definition of both the domain and range

The Domain: This is all the values that are inputed into the function, or found on the graph. In most cases, these are referred to as the X-values.

The Range: These are all of the outputted values. Most commonly these are considered the Y-values of a function.

R- All real numbers, this is used to to set the parameters for where the domain and range start and stop.
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Now that we've covered the basic definitions of these concepts, it is important to comprehend them in a real life analogy.

Imagine the total population of your school, this is the equivalent of R, all real numbers.

Now consider within your class who your friends are, and whom you dislike. We will consider your friends as the domain, and those you dislike as your range. We say that out of all the students are the school, (R), you are only friends with Matt, Alex, Reggie and Scotty. This is the domain and we will illustrate it as Domain (Matt, Alex, Reggie, Scotty) The same can be done for the range. These intervals help us determine who your friends with and who you dislike, just like in a graph, they help us determine which values are included, and which are excluded from the function.
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This is our first example of domain and range. you can clearly see it illustrated in this graph. However, this is only a representation of domina and range. Next class we will learn how to properly write it in set builder and interval notation.

We will countinue with this concept next week. Until then don't get in any trouble with the Robocops.