Answer:
D = {0 , 1 , 2 , 3 , 4 , 5} and R = {1 , 2 , 4 , 8 , 16 , 32} ⇒ answer D
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}