https://file.aiquickdraw.com/mathbot/file/17281866062146ywntwct.jpg

From the graph you provided, we are asked to determine the **domain** and **range** of the function \( g \). Let's analyze it step by step.

### Domain:
The domain refers to all the possible values of \( x \) for which the function is defined.

- The function \( g \) starts at \( x = -5 \) (inclusive) and ends at \( x = 5 \) (inclusive). We observe that for all values of \( x \) between \( -5 \) and \( 5 \), the graph is continuous and well-defined.

Therefore, the domain of \( g \) is:
\[
\boxed{[-5, 5]}
\]

### Range:
The range refers to all the possible values of \( y \) that the function can take.

- The lowest point of the graph appears to be at \( y = -3 \), and the highest point appears to be at \( y = 4 \).
- As the graph spans continuously from \( y = -3 \) to \( y = 4 \), these values are included.

Thus, the range of \( g \) is:
\[
\boxed{[-3, 4]}
\]

### Final Answer:
- **Domain:** \( [-5, 5] \)
- **Range:** \( [-3, 4] \)

Let me know if you'd like more details on any part of this solution!

### Follow-up Questions:
1. What is the significance of the domain and range in a real-world context?
2. Can you explain how the domain might change for different types of functions?
3. How would you find the domain and range algebraically without a graph?
4. What are some functions that have restricted domains, such as square roots or logarithms?
5. How do vertical asymptotes affect the domain of a function?

### Tip:
When determining the domain and range from a graph, always focus on the horizontal span (domain) and the vertical span (range) of the curve.

Write the domain and range of the function g based on the graph.

Learn how to find the domain and range of a function based on its graph. This example covers key concepts in understanding the continuous behavior of a function and identifying its domain and range, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation