College Algebra, Chapter 2, Review Exercises, Section Review Exercises, Problem 24

Sketch the graph of the equation $y = -\sqrt{1-x^2}$ by making a table and plotting points.

We have,

$
\begin{equation}
\begin{aligned}
1 - x^2 &\geq 0\\
\\
(1-x)(1+x) &\geq 0
\end{aligned}
\end{equation}
$

The factors on the left hand side is $1-x$ and $1+x$. These factors are zero when $x$ is $1$ and $-1$, respectively. These numbers divide the number line into intervals,
$(-\infty, -1], [-1,1], [1,\infty)$
By testing some points on the interval,



Thus, the domain is $[-1,1]$

Let


$
\begin{array}{|c|c|}
\hline\\
x & y = - \sqrt{1-x^2}\\
\hline\\
-1 & 0\\
\\
-0.75 & -0.661\\
\\
-0.5 & -0.866\\
\\
-0.25 & -0.968\\
\\
0 & -1\\
\\
0.25 & -0.968\\
\\
0.5 & -0.866\\
\\
0.75 & -0.661\\
\\
1 & 0\\
\\
\hline

\end{array}
$