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Task Background:
Part I: Suppose you are developing a statistical database in which information about professional football teams and records are stored.
Consider the following 2 sets of data that list football teams and quarterbacks:
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Order Paper NowD = {Jets, Giants, Cowboys, 49’ers, Patriots, Rams, Chiefs}
Q = {Tom Brady, Joe Namath, Troy Aikman, Joe Montana, Eli Manning}
- Using D as the domain and Q as the range, show the relation between the 2 sets, with the correspondences based on which players are (or were) a member of which team(s). (You can use http://www.pro-football-reference.com to find out this information). Show the relation in the following forms:
- Set of ordered pairs
- Directional graph
- Is the relation a function? Explain.
- Now, use set Q as the domain, and set D as the range. Show the relation in the following forms:
- Set of ordered pairs
- Directional graph
- Is the relation a function? Explain.
Part II:
Mathematical sequences can be used to model real life applications. Suppose you want to construct 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 you need 50 rows of seats.
(a) Write the sequence for the number of seats for the first 5 rows
(b) How many seats will be in the last row?
(c) What will be the total number of seats in the theater?
