College Algebra, Chapter 2, 2.2, Section 2.2, Problem 34

Make a table of values and sketch the graph of the equation $y = x^3 - 1$. Find the $x$ and $y$ intercepts.

$
\begin{array}{|c|c|}
\hline\\
\text{Let } x & y = x^3 - 1 \\
\hline\\
-3 & -28 \\
\hline\\
-2 & -9 \\
\hline\\
-1 & -2 \\
\hline\\
1 & 0 \\
\hline\\
2 & 7 \\
\hline\\
3 & 26\\
\hline
\end{array}

$

To solve for $y$ intercept, we set $x = 0$


$
\begin{equation}
\begin{aligned}

y =& 0^3 - 1
\\
\\
y =& -1

\end{aligned}
\end{equation}
$


Thus, the $y$ intercept is at $(0,-1)$

To solve for the $x$ intercept, we set $y = 0$


$
\begin{equation}
\begin{aligned}

0 =& x^3 - 1
\\
\\
x^3 =& 1
\\
\\
x =& \sqrt[3]{1}
\\
\\
x =& 1

\end{aligned}
\end{equation}
$


The $x$ intercept is at $(1, 0)$