CH1 Real World Function

In this Project, we had to find an example of a real world function, and I chose the page number of a book called Pre-Calculus: Graphical, Numerical, Algebraic by Demana, Warts, Foley, and Kennedy.

Every time we turn the page in the book, we land on a certain section of a certain chapter, and in this case, I chose chapter 1.

For my example of a function (on the left) there are a certain amount of page numbers to be turned to end up on a certain section, but every time i flip a certain amount of pages to get to a chapter, I always started in the beginning page. A Function is a set of all points (x,F(x)) where each input as "x" has exactly one output which is represented as Y or F(x).

For my example of a Relation (on the right) which is a set of ordered pairs, which is not a Function, I used the same book to flip 70 pages to get to chapter 1.1, ;however, when I flipped 70 pages again, I did not land on chapter 1.1, i ended up on chapter 1.5, and when I flipped 70 pages again, I was found on a whole new chapter. This shows that it is not a relation because for every 70 pages i turn, i get more than one output, which goes against the rule of a function having one output for every input, in addition, it also fails the vertical line test, therefore, it is a relation.

The Independent variable in these two graphs are the page numbers, and the dependent variable were the sections of the chapter.

When i graphed out all of the coordinates, for my function example, i got a line that passes the vertical line test, meaning, it is a function. I got the Domain: [0,163] and the Range: Chapters: (1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7) U (2.3), but the relevant Domain to the function on the left was [70,163], and the relevant Domain for the relation on the right was only 70. This shows a basic idea of the difference between a Function and a Relation.