 piecewise-defined function is shown below. 



If the domain of 
 is {-6, -1, 2, 4, 12}, then what is the range of 
 ?
{-6, -1, 2, 4, 12}
{-12, -2, 1, 3, 6}
{-6, -3, -1, 2, 12}
{1, 2, 3, 6, 12}


To determine the range of a piecewise-defined function, we first need to evaluate the function at the given values of the domain. You mentioned that the domain of the function is \(\{-6, -1, 2, 4, 12\}\), but you haven't provided the actual piecewise function itself. Typically, a piecewise function is defined with different rules depending on the input value, so let's outline the general steps to find the range:

### Steps:
1. **Identify the piecewise rules**: Determine which rule applies to each value of the domain.
2. **Substitute each domain value into the correct rule**: For each element in the domain, plug it into the corresponding piecewise rule.
3. **Find the output for each domain value**: These outputs will make up the range.

However, since no piecewise function is provided, I'll guide you with general options based on common interpretations of piecewise functions.

#### Assuming the following scenarios:
1. If the piecewise function maps \(\{-6, -1, 2, 4, 12\}\) to specific outputs, you would evaluate each value according to the rules of the function.

Now, based on the options provided:
- Option 1: \(\{-12, -2, 1, 3, 6\}\)
- Option 2: \(\{-6, -3, -1, 2, 12\}\)
- Option 3: \(\{1, 2, 3, 6, 12\}\)

Without the explicit function, you can compare typical behavior in piecewise functions and recognize patterns based on outputs from common mathematical expressions, like linear or quadratic sections.

If you have the function or more details, I can help evaluate the exact range.

Would you like more details on piecewise functions or share the specific function? If not, I can help by reviewing some of these output choices more carefully.

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**Relative Questions:**
1. How do piecewise functions handle different intervals?
2. What are some common examples of piecewise-defined functions?
3. How do you interpret function notation when different rules apply for different inputs?
4. How do you identify if a function is continuous or not from its piecewise definition?
5. Can the domain of a piecewise function include a single point or must it always be an interval?

**Tip**: Always check which rule of the piecewise function applies to each element of the domain before plugging values in.

A piecewise-defined function is shown below. If the domain is {-6, -1, 2, 4, 12}, then what is the range?

Understand how to find the range of a piecewise-defined function when provided with a specific domain. This problem helps explore the concept of domain and range in piecewise functions and is suitable for students in Grades 9-11.

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