Question

How do you find the domain and range of `x^2+y^2=9`?

Answer 1

If you plug this graph into a calculator, you will find that it is a graph of a circle.

Circles have the formula `x^2 + y^2 = r^2` if they are centered at the origin.

From that, we can find that the radius is 3, and it is centered at the origin.

To find the domain and range, we just find the largest and smallest x and y values.

Since the radius is 3, and the graph is centered at the origin, the largest x value is 3. Similarly, the smallest x value is -3.

The domain is `-3 <= x <= 3`

We can use the same thing for the range. The radius is 3, so the largest and smallest values of the y will be 3 and -3.

The range is `-3 <= y <= 3`