Graph of $y = \sqrt{1 - x^2}$ (Upper Semicircle)

Squaring $y = \sqrt{1 - x^2}$ gives the equation of the circle of radius $1$ centered at the origin.

Since $y \geq 0$, the graph is only its upper half. The expression under the radical must be non-negative, so the domain is $-1 \leq x \leq 1$ and the range is $0 \leq y \leq 1$.