https://file.aiquickdraw.com/mathbot/file/17272189178126nmw8dg5.jpg

The image shows a graph of a semicircle above the x-axis. The graph is symmetric with respect to the y-axis, and the semicircle appears to be centered at the origin \((0,0)\), with a radius of 5 (since it spans from \(-5\) to \(5\) on the x-axis). 

To find the domain of this function, we need to determine the possible values of \(x\) for which the function is defined. Since the function represents the upper half of a circle, its domain corresponds to the x-values that lie between \(-5\) and \(5\).

### Domain:
The function is defined for all \(x\) values in the interval \([-5, 5]\).

Thus, the domain of the function is:

\[
\boxed{[-5, 5]}
\]

Would you like further explanation or details on how this domain was calculated?

### 5 Related Questions:
1. What is the range of the function shown in the graph?
2. How would the domain change if the semicircle were below the x-axis?
3. How can you find the equation of the semicircle given the radius and center?
4. What would the domain and range be if the graph showed a full circle instead of a semicircle?
5. How does the radius of the circle affect the domain and range of the function?

### Tip:
When determining the domain of a function from a graph, focus on the x-values for which the graph exists on the coordinate plane.

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

Determine the domain of a function by analyzing the graph of a semicircle. This problem involves understanding the properties of circles and functions, including how to find the domain from a graph. Suitable for students in Grades 9-11.

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