https://file.aiquickdraw.com/mathbot/file/1731131995849918kk7tj.jpg

To identify which graph represents an absolute value equation and determine its domain and range, let's examine each option.

An absolute value function typically has a "V" shape, represented by the equation \( y = |x| \). This shape occurs because absolute value outputs non-negative values.

### Analyzing the Graphs

1. **Graph (1)**: This graph appears to open upward in a curve, not a V shape, which resembles a quadratic function. It's unlikely to represent an absolute value function.

2. **Graph (2)**: This graph has a clear "V" shape, indicating it is likely an absolute value function.

3. **Graph (3)**: This graph has a parabolic shape, opening downwards, which is characteristic of a quadratic function, not an absolute value function.

4. **Graph (4)**: This graph is linear and does not exhibit the typical "V" shape of an absolute value function.

### Conclusion

The correct answer is **Graph (2)**, as it has the characteristic "V" shape.

#### Domain and Range for Graph (2):
- **Domain (D)**: The domain of an absolute value function is all real numbers, so \( D = (-\infty, +\infty) \).
- **Range (R)**: Since the absolute value function produces non-negative outputs, the range is \( R = [0, +\infty) \).

### Answer:
The answer is **b) Second graph: \( D: (-\infty, +\infty) \), \( R: [0, +\infty) \)**.

Would you like more details on this explanation or have any questions?

#### Further Related Questions:
1. What are the transformations of an absolute value function?
2. How do you determine the vertex of an absolute value graph?
3. What is the effect of adding a constant to an absolute value function?
4. How do you find the domain and range of a quadratic function?
5. How does the graph of \( y = |x| \) compare to that of \( y = x^2 \)?

#### Tip:
When identifying absolute value graphs, look for the distinctive "V" shape, which reflects the function's non-negative output characteristic.

Which graph represents an absolute value equation? Write its domain and range.

Learn how to identify absolute value functions in graphs and determine their domain and range. This problem helps students recognize the distinct 'V' shape of absolute value functions and understand domain and range concepts. Suitable for students in Grades 7-9.

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