Part I
1. Given the sets
Domain
D = {Jets, Giants, Cowboys, 49’ers, Patriots, Rams, Chiefs}
Range
Q = {Tom Brady, Joe Namath, Troy Aikman, Joe Montana, Eli Manning}
Set of ordered pairs
{(Jets, Joe Namath), (Giants, Eli Manning), (Cowboys, Tom Aikman), (49’ers, Joe Montana), (Patriots, Tom Brady), (Rams, Joe Namath), (Chiefs, Joe Montana)}.
Directional Graph
Jets Joe Namath
Giants Eli Manning
Cowboys Troy Aikman
49’ers Joe Montana
Patriots Tom Brady
Rams
Chiefs
2. Is this relation a function?
This relation is a function. There is a unique connection from team to player. 3. Using Q as the domain and D as the range
Set of ordered pairs
{(Joe Namath, Jets), (Eli Manning, Giants), (Troy Aikman, Cowboys), (Joe Montana, 49ers), (Tom Brady, Patriots), (Joe Namath, Rams), (Joe Montana, Chiefs)}.
4. is this relation a function?
Joe Montana and Joe Namath don’t have a unique relationship to a team. It is a one to two relation with elements in the range and because of that this relation is not a function.
Part II
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.
Write the sequence for the number of seats for the first 5 rows
C(1) = 16 + 4(1) = 16 + 4 = 20 seats in the first row
C(2) = 16 + 4(2) = 16 + 8 = 24 seats in the second row
C(3) = 16 + 4(3) = 16 + 12 = 28 seats in the third row
C(4) = 16 + 4(4) = 16 + 16
