https://file.aiquickdraw.com/mathbot/file/1726521860899forb76iq.jpg

The graph in the image represents a function that starts at \(x = 1\) and increases to the right along the positive \(x\)-axis. To find the domain of the function, we need to identify the set of all possible \(x\)-values for which the function is defined.

### Domain Analysis:
- The function begins at \(x = 1\) (including \(x = 1\)) and continues indefinitely to the right (as \(x \to \infty\)).
- The smallest \(x\)-value is \(x = 1\), and there is no upper bound for \(x\).

Thus, the domain of the function is:
\[
[1, \infty)
\]

This means the function is defined for all \(x\)-values starting from 1 and greater.

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:
1. How do you find the range of a function from its graph?
2. What are the differences between open and closed intervals in domain notation?
3. How would the domain change if the graph had a vertical asymptote?
4. Can a function have a domain of all real numbers? Give an example.
5. How would the domain change if the function started at \(x = -1\)?

**Tip:** Always pay close attention to whether the graph includes the endpoints (solid vs. open points), as this will affect the domain interval!

What is the domain of the function shown in the graph below?

Learn how to determine the domain of a function from its graph. This problem illustrates a function that starts at x = 1 and continues to positive infinity, suitable for students in Grades 9-12.

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