Final answer:
The domain of the shipping service's postage charge function is the set {1, 2, 3, 4, 5}, representing the weights of packages in whole pounds. The range is the set {3, 5, 7, 9, 11}, corresponding to the cost in dollars to ship packages weighing 1 through 5 pounds, respectively.
Step-by-step explanation:
The domain of the function described for the shipping service's postage charge can be thought of as the possible weights of the packages (in pounds), which in this case is 1 to 5 pounds. The domain is a set of input values consisting of whole numbers from 1 to 5 because the service only charges for whole-pound increments. To find the domain, consider the weight of the package as 'x'. Here 'x' must be greater than or equal to 1 but less than or equal to 5. So, the domain is {1, 2, 3, 4, 5}.
For the range of the function, which represents the cost to ship a package, we calculate the cost as $3 for the first pound and $2 for each additional pound. So the charges will be:
- For 1 pound: $3 (just the first pound rate)
- For 2 pounds: $3 + $2 = $5
- For 3 pounds: $3 + $2*2 = $7
- For 4 pounds: $3 + $2*3 = $9
- For 5 pounds: $3 + $2*4 = $11
Thus, the range of the postage charge is {3, 5, 7, 9, 11}, which corresponds to each value in the domain respectively.
To summarize, the domain is the set {1, 2, 3, 4, 5} and the range is the set {3, 5, 7, 9, 11} for the shipping service's postage charge function based on weight.