Here is the equation of the whole circle.
Now find y1 and y2, the negative square root would be the botom half of the circle.
Lets find the equation of the full circle first.
Rearrange for Y
When it is in this form, the range and domain are defined as follows:
The domain is all possible values that x can take
The range is all possible values that y can take
Because it is a circle with radius 5, centered around (3,0); you know the domain and range are:
You want the bottom half of the circle, which is the part where Y<0.
Hopefully, you can see that
Domain: (the same)
Range: (bottom half only)
This is much easier to draw than do in your head. I'll try to attach an image later
edit too slow