The postal service charges $2 to ship packages up to 5 ounces in weight, and $0.20 for each additional ounce up to 20 ounces. After that, they charge $0.15 for each additional ounce.

What is the domain of this relation?

The domain of this relation refers to the possible weights of the packages for which the postal service charges a shipping fee.

Given the problem, we can break it down as follows:
1. The service charges $2 for packages weighing **up to 5 ounces**.
2. For packages **between 5 and 20 ounces**, the charge increases by $0.20 for each additional ounce.
3. For packages **above 20 ounces**, the charge increases by $0.15 for each additional ounce.

Since there is no stated upper limit to the weight of a package, the domain includes all weights greater than 0 ounces.

### Domain:
The domain of this relation is **all positive real numbers** because packages can weigh any amount greater than zero, i.e., $ (0, \infty) $.

Would you like to explore the pricing structure for specific package weights, or do you have other questions?

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Here are 5 related questions:
1. How would the postal service's price change for a package weighing 10 ounces?
2. What is the mathematical expression for the shipping cost of a package weighing over 20 ounces?
3. Can you find the shipping cost of a 25-ounce package using this model?
4. What if the package weighed exactly 5 ounces—what would the cost be?
5. How would the domain change if there were a maximum allowable package weight?

**Tip:** When analyzing domains, always check for any constraints or limits mentioned in the problem, such as weight limits or pricing caps.

The postal service charges $2 to ship packages up to 5 ounces in weight, and $0.20 for each additional ounce up to 20 ounces. After that, they charge $0.15 for each additional ounce. What is the domain of this relation?

Understand how to determine the domain of a shipping cost function, where charges are based on package weight. This problem explores key mathematical concepts such as the domain of functions and piecewise functions, applicable for Grades 9-11.

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