Question

What is the domain and range of the function `x^2+y^2 = 1`?

Answer 1

Both domain and range is `[-1,+1]`

Explanation:

The equation of a circle centred at point `(a,b)` with radius `r` is:
`(x-a)^2 + (y-b)^2 =r^2`

`:. x^2+y^2 = 1` is the equation of a circle centred at the origin with radius 1.

Hence, domain and range are both `[-1, +1]`

We can see this from the graph of `x^2+y^2=1` below.

graph{x^2+y^2=1 [-3.08, 3.08, -1.54, 1.54]}