https://file.aiquickdraw.com/mathbot/file/1729433592255085qpmd6.jpg

To determine the domain and range of the piecewise function shown in the coordinate plane:

### **Domain:**
The domain refers to all possible values of \( x \) for which the function is defined. Looking at the graph, the function starts at \( x = -5 \) (open circle) and continues to \( x = 3 \) (closed circle).

Thus, the domain is:
\[ -5 < x \leq 3 \]

### **Range:**
The range refers to all possible values of \( y \) that the function outputs. From the graph, the smallest value of \( y \) is \( y = -5 \) (open circle) and the largest value is \( y = 3 \) (closed circle).

Thus, the range is:
\[ -5 < y \leq 3 \]

### Final answer:
- **Domain:** \( -5 < x \leq 3 \)
- **Range:** \( -5 < y \leq 3 \)

Do you want more details or have any questions?  
Here are 5 related questions to explore further:
1. How would you write the piecewise function for this graph?
2. How do open and closed circles affect the domain and range of a function?
3. What is the significance of having a piecewise function compared to a continuous function?
4. How can you determine if a piecewise function is continuous at a certain point?
5. How can you graph a more complex piecewise function given its equation?

**Tip:** Always observe the endpoints carefully to determine whether they are included or excluded when calculating domain and range.

What is the domain and range of the piecewise function shown on the coordinate plane?

Learn how to determine the domain and range of a piecewise function from its graph. This example shows a function defined from x = -5 to x = 3 with specific y-values ranging from -5 to 3. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation