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Choose the correct formula for the function.

The image shows a graph with two line segments plotted on a Cartesian plane. The task is to determine the correct formula (or equations) that represent the function shown.

### Analyzing the Graph:

1. **Line Segment 1**:
   - This line segment is located on the x-axis between x = -4 and x = -2.
   - The y-coordinate remains constant at y = -3 throughout this segment.
   - This can be represented by the equation \( y = -3 \) for \( -4 \leq x \leq -2 \).

2. **Line Segment 2**:
   - This line segment is located on the x-axis between x = 2 and x = 4.
   - The y-coordinate remains constant at y = 1 throughout this segment.
   - This can be represented by the equation \( y = 1 \) for \( 2 \leq x \leq 4 \).

### Formula for the Function:
The function consists of two parts:
- \( y = -3 \) for \( -4 \leq x \leq -2 \)
- \( y = 1 \) for \( 2 \leq x \leq 4 \)

These can be combined into a piecewise function:

\[
f(x) = \begin{cases} 
-3 & \text{for } -4 \leq x \leq -2 \\
1 & \text{for } 2 \leq x \leq 4 \\
\text{undefined} & \text{otherwise}
\end{cases}
\]

This piecewise function is the correct formula representing the graph.

Would you like further details or have any questions about this solution? Here are some related questions you might find interesting:

1. How do you determine the equation of a line segment on a graph?
2. What is a piecewise function and how is it represented?
3. How can a function be discontinuous as seen in this graph?
4. What are some real-world applications of piecewise functions?
5. How do you graph a piecewise function with more complex conditions?

**Tip:** When graphing functions, always check the intervals over which each part of the function is defined to ensure you capture the correct behavior across the domain.

Explore how to identify the correct formula for a piecewise function based on a graph. This problem involves understanding piecewise functions and graphing on the Cartesian plane, making it suitable for students in Grades 9-11.

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