Relations, Functions, Sequences, and Graphs

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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:

D = {Jets, Giants, Cowboys, 49’ers, Patriots, Rams, Chiefs}

Q = {Tom Brady, Joe Namath, Troy Aikman, Joe Montana, Eli Manning}

  1. 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 to find out this information). Show the relation in the following forms:
    • Set of ordered pairs
    • Directional graph
  2. Is the relation a function? Explain.
  3. 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
  4. 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?

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