MATH SOLVE

4 months ago

Q:
# There are 32 teams participating in a single-elimination soccer tournament, in which only the winning teams from each round progress to the nextround of the tournamentThe graph shows the number of teams, fx) that are still in the tournament after x rounds have been completedf(x)

Accepted Solution

A:

Answer: D = {0 , 1 , 2 , 3 , 4 , 5} and R = {1 , 2 , 4 , 8 , 16 , 32} ⇒ answer DStep-by-step explanation:* Lets talk about the domain and the range of a function- The domain is the input values- The range is the output values- f(x) = y, x is the input then x is the domain of the function and y is the output then y is the range of the function- Example:# If x = {2 , 3 , 5) and f(x) = 2x- The input is x to find f(x) substitute the values of x in f(x) - f(2) = 2(2) = 4 , f(3) = 2(3) = 6 , f(5) = 2(5) = 10- The output is f(x) = {4 , 6 , 10}- From all steps above the domain of f(x) is {2 , 3 , 5) and the range is {4 , 6 , 10}* Lets solve the problem- There are 32 teams participating in a single-elimination soccer tournament- x is the number of rounds- f(x) is the number of teams- only the winning teams from each round progress to the next
round of the tournament* Lets look to the graph and find the domain and the range- The domain the the values of x and the range is the values of f(x)∵ At x = 0 then f(0) = 32 ⇒ 32 teams inter the 1st round∵ At x = 1 then f(1) = 16 ⇒ 16 teams inter the 2nd round∵ At x = 2 then f(2) = 8 ⇒ 8 teams inter the 3rd round∵ At x = 3 then f(3) = 4 ⇒ 4 teams inter the 4th round∵ At x = 4 then f(4) = 2 ⇒ 2 teams inter the 5th round∵ At x = 5 then f(5) = 1 ⇒ 1 team in win- From all above:∴ The domain is {0 , 1 , 2 , 3 , 4 , 5} and the range is {1 , 2 , 4 , 8 , 16 , 32}* D = {0 , 1 , 2 , 3 , 4 , 5} and R = {1 , 2 , 4 , 8 , 16 , 32}