Part A: Find the intervals where the piecewise defined function is negative, and enter your answer in interval notation. If none exist, enter NONE. Part B: Find the intervals where the piecewise defined function is increasing, and enter your answer in interval notation. If none exist, enter NONE.
Part A: Find the intervals where the piecewise defined function is negative, and enter your answer in interval notation. If none exist, enter NONE. Part B: Find the intervals where the piecewise defined function is increasing, and enter your answer in interval notation. If none exist, enter NONE.
Part A: Find the intervals where the piecewise defined function is negative, and enter your answer in interval notation. If none exist, enter NONE. Part B: Find the intervals where the piecewise defined function is increasing, and enter your answer in interval notation. If none exist, enter NONE.
Part A: Find the intervals where the piecewise defined function is negative, and enter your answer in interval notation. If none exist, enter NONE.
Part B: Find the intervals where the piecewise defined function is increasing, and enter your answer in interval notation. If none exist, enter NONE.
Transcribed Image Text:### Graph of a Piecewise Defined Function
The image presents a graph of a piecewise defined function on a coordinate plane. Below is a detailed description of the graph:
#### Components of the Graph:
1. **Piece 1 (Left Curve):**
- **Shape:** This section is a downward concave curve located on the left side of the graph.
- **Domain:** The curve extends from \(-\infty\) to approximately \(x = -3\).
- **Behavior:** As \(x\) approaches \(-\infty\), the curve approaches \(-\infty\). The left endpoint appears to be at \(x = -3\) with an open circle, indicating that it does not include this point.
2. **Piece 2 (Line Segment):**
- **Shape:** A linear segment spans from \((x \approx -3, y = 0)\) to \((x = 0, y = -2)\).
- **Endpoints:** This segment includes the point at \(x = 0\) with a closed circle and the point at \(x \approx -3\) with an open circle.
3. **Piece 3 (Line Segment):**
- **Shape:** Another linear segment runs from \((x = 0, y = 2)\) to \((x = 4, y = 0)\).
- **Endpoints:** This segment includes the point at \(x = 0\) with an open circle and the point at \(x = 4\) with a closed circle.
4. **Piece 4 (Right Line):**
- **Shape:** A linear line starts at \((x = 4, y = 2)\) and extends to the right.
- **Domain:** The line extends from \(x = 4\) to \(+\infty\).
- **Endpoint:** This piece begins with a closed circle at \(x = 4\).
This graph provides a visual representation of a function composed of multiple segments, each defined on specific intervals. The open and closed circles indicate whether the endpoints are included in each piece. This kind of graph is typical in piecewise functions where different rules apply to different portions of the domain.
Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.
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