Sean Graham
IP2
MATH203-1501B-02
Part I Part one of the assignment is to show the relation between the 2 sets of data, with the correspondences based on which players are or were a member of which teams. We are to show the relation in both a set of ordered pairs, and as a directional graph. Set D has the Jets, the Giants, the Cowboys, the 49ers, the Patriots, the Rams, and the Chiefs. Set Q has Tom Brady, Joe Namath, Troy Aikman, Joe Montana, Eli Manning. The first step is to assign a domain and range. For the first task D is the domain and Q is the range. The Set of ordered pairs of the domain and range would look like the following: {(Patriots, Tom Brady), (Jets, Joe Namath), (Cowboys, Troy Aikman), (49ers, Joe Montana), (Giants, Eli Manning), (Rams, Joe Namath), (Chiefs, Joe Montana)}. The graph of these sets is on the next page.

The direction graph of this set would look like the following:

Part two asks to explain if the relation is or is not a function. This relation would be identified as a function. It is a function because each x value, which is the domain, has only one y value, which is the range. In regards to the example/ at hand, each team only had the one player. Part three asks to swap the domain and range used earlier and to show it again in a set of ordered pairs, and as a directional graph. The Set of ordered pairs of the domain and range would look like the following: {(Tom Brady, Patriots), (Joe Namath, Jets), (Troy Aikman, Cowboys), (Joe Montana, 49ers), (Eli Manning, Giants), (Joe Namath, Rams), (Joe Montana, Chiefs)}.
The direction graph of this set would look like the following:
PART 2
PART 2

Part 4 asks to explain if the relation is or is not a function. This relation would not be identified as a function. It is not a function because each x value, which is the domain, has more than one y value, which is the range. In regards to the example/ at hand, some players have multiple teams.
PART II
Part 2 is using an example of constructing a movie theater in your town. The number of seats in each row can be modeled by the formula C_n = 16 + 4n, when n refers to the nth row, and needing 50 rows of seats. The first problem is to write a sequence for the number of seats for the first 5 rows. The first row will have 20 seats. The second row will have 24 seats. The third row will have 28 seats. The fourth row will have 32 seats. The fifth row will have 36 seats. The sequence would look like: {20, 24, 28, 32, 36}. The second problem is to find how many seats will be in the last row. Using the equation, the number of seats would equal 16 plus 4 times 50. This means in the last row, there would be a total of 216 seats in the final row. Part three is to find the total number of seats in the theaters. To find the total chairs, we must use the sum formula, by taking the total amount of chairs in the last row and adding it to the chairs in the first row, which is 236. We then multiply by the amount of rows, which is 50. This brings us to a total of 11800. This number is then divided by 2, which brings a grand total of 5900 seats in the theater. To verify we have the correct answer, I also completed the function for each row and added the sums, which gave me the same answer.