1. The problem is to analyze the function $y = \sqrt{1 - x^2}$. 2. This function represents the upper half of a circle centered at the origin with radius 1, because the equation $x^2 + y^2 = 1$ describes a circle. 3. The square root restricts $y$ to non-negative values, so $y \geq 0$. 4. The domain is all $x$ such that the expression under the square root is non-negative: $1 - x^2 \geq 0$. 5. Solving for $x$, we get $-1 \leq x \leq 1$. 6. The range is $0 \leq y \leq 1$. 7. The function intercepts the axes at $x=0$, $y=1$ (top of the circle), and at $x=\pm 1$, $y=0$ (ends of the semicircle). 8. The function has a maximum (extremum) at $x=0$, where $y=1$. 9. The function is symmetric about the y-axis because it depends on $x^2$. Final answer: The function $y = \sqrt{1 - x^2}$ is the upper semicircle of radius 1 centered at the origin with domain $[-1,1]$ and range $[0,1]$.