https://file.aiquickdraw.com/mathbot/file/1724947579708jym6q6dh.jpg

Select the correct answer below:

(
0
,
5
)

[
−
2
,
3
)

[
0
,
5
]

(
−
2
,
3
)

[
−
2
,
3
]

[
0
,
5
)

To determine the domain of the function \( f(x) \) from the graph, we need to identify all the \( x \)-values for which the function is defined.

Looking at the graph:

- The function starts at \( x = -2 \) (inclusive), as the graph begins there and the point is solid.
- The function ends at \( x = 5 \) (exclusive), as the graph stops there and the point is not solid, indicating that \( x = 5 \) is not included in the domain.

Thus, the domain of the function \( f(x) \) is the interval \([ -2, 5 )\).

This matches one of the given choices: \[ [-2, 5) \].

Would you like more details or have any questions? Here are some additional questions to consider:

1. How would you find the range of the function from the graph?
2. What would the domain be if the graph continued indefinitely?
3. Can a function have more than one interval in its domain?
4. What does the open interval notation signify compared to closed interval notation?
5. How does the graph help determine the points where the function is not defined?

**Tip:** Always check whether endpoints are included in the domain by examining if the graph has solid or open points at those ends.

Learn how to determine the domain of a function from its graph with detailed explanations and examples. This problem focuses on interval notation, identifying endpoints, and understanding function domains from graphical representations. Suitable for high school students studying functions and graph theory.

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