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.