https://file.aiquickdraw.com/mathbot/file/17364740484952gz8hqju.jpg

The task is to determine the **range** of the given graph.

### Step-by-step solution:
1. **Definition of Range**:
   The range of a function is the set of all possible \(y\)-values (outputs) that the function can take. To find the range, observe the vertical extent of the graph.

2. **Analyzing the Graph**:
   - The graph has a minimum \(y\)-value at approximately \(-10\) (the lowest point of the curve).
   - The graph extends upwards to a maximum \(y\)-value of \(10\), as indicated by the open circle near \(y = 10\).
   - The open circle at \(y = 10\) shows that \(y = 10\) is not included in the range.
   - The graph continues smoothly between \(y = -10\) and \(y = 10\), so all \(y\)-values in this interval are included except \(10\).

3. **Conclusion**:
   The range of the graph is:
   \[
   [-10, 10)
   \]
   This means \(y\) can take any value from \(-10\) to \(10\), including \(-10\) but excluding \(10\).

---

### Do you have any questions or want further clarification?

### Related Questions:
1. What is the difference between the range and domain of a function?
2. How would the range change if the open circle at \(y = 10\) were filled?
3. Can the range of a graph include gaps or discontinuities? Explain with examples.
4. How can you determine if a graph has an open or closed interval for its range?
5. How does the behavior of the graph near the edges influence the range?

### Tip:
When identifying the range of a function, always check for open or closed points and note whether the graph extends infinitely or is bounded within a specific interval.

Determine the range of the following graph:

Learn how to determine the range of a function by analyzing its graph. This step-by-step guide explains the concept of range, including open and closed intervals. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation