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The problem presented describes the cost of mailing a package, which is initially $2.54 for up to 3 ounces, with an additional $0.20 for each ounce (or fraction thereof) beyond 3 ounces. The question asks which option best describes the range of the function representing the cost as a function of the weight (in ounces) of the package.

Let's break this down:

1. **Cost for up to 3 ounces**: The cost remains constant at $2.54. 
2. **Cost for more than 3 ounces**: For each additional ounce, the cost increases by $0.20.

Thus, the cost function starts at $2.54 and increases by $0.20 for each full or partial ounce after 3 ounces. The range is composed of specific dollar values that the function can take, corresponding to the base price plus increments of $0.20.

### Analysis of the Answer Choices:

- **A.** The range is positive real numbers: 
   - This is incorrect because the cost increases in discrete steps of $0.20, not continuously across all real numbers.

- **B.** The range is positive integers:
   - This is incorrect because the cost is not restricted to whole numbers. It can take values like $2.54, $2.74, etc.

- **C.** The range is values of the form $ 2.54 + 0.2x $, where $ x $ is a nonnegative real number:
   - This is incorrect because the increments occur only at specific points (for each additional ounce), not for all nonnegative real values of $ x $.

- **D.** The range is values of the form $ 2.54 + 0.2x $, where $ x $ is a nonnegative integer:
   - This is correct. The cost starts at $2.54 and increases by $0.20 for each additional ounce or fraction thereof, which means $ x $ must be a nonnegative integer representing the number of additional ounces.

### Correct Answer:
**D** is the correct choice.

Do you need any further explanation or details?

### Here are 5 questions related to this topic:
1. How would the function change if the base cost for the first 3 ounces was different?
2. What would the range be if the increment for each additional ounce was $0.25 instead of $0.20?
3. How could you express the function for a general mailing cost problem?
4. How does the graph of this cost function differ from a continuous function like $ f(x) = 2.54 + 0.2x $?
5. What is the domain of this cost function?

**Tip**: The range of a function refers to all possible output values the function can take

In 2016, the cost to mail a package was $2.54 for up to 3 ounces, plus an additional cost of $0.20 for each additional ounce or portion of an ounce less than a full ounce. A portion of the graph of this relationship is given with cost, in dollars, as a function of ounces. Which of the following describes the restrictions on the range for such a function?

Explore how the cost of mailing a package in 2016 is calculated, with a base price of $2.54 for up to 3 ounces and a $0.20 increase for each additional ounce. Learn how to determine the range of values based on this piecewise cost function.

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