Answer:
The domain is the set of all integers from 0 to 14
The range is the set of all multiples of 5 between 0 and 70
Step-by-step explanation:
Domain and Range of a Function
The Domain of a Function is the set of values the input variable x takes.
The Range of a Function is the set of values the function takes when x moves into the function's domain.
Coach Harper can buy softballs at $5 each but he has a limit of $72 to spend on them. This situation is written as the following inequality:
5x ≤ 72
Where x is the number of softballs coach Harper can buy. Solving:
x ≤ 72/5
x ≤ 14.4
Since the number of balls must be an integer quantity and cannot be negative:
0 ≤ x ≤ 14
This means the maximum number of softballs coach Harper can buy is 14.
Thus, the domain is the set of all integers from 0 to 14
When 0 balls are bought, $0 are spent
When 1 ball is bought, $5 are spent
When 2 balls are bought, $10 are spent
Following that sequence with the maximum number of softballs:
When 14 balls are bought, $70 are spent
Note the cost can only be a multiple of 5 between 0 and 70, thus the range is the set of all multiples of 5 between 0 and 70.
