Graph the equation
Y=x^3-3
To graph the equation \(y = x^3 - 3\), we will plot several points and then connect them to form a curve.
We can start by selecting some values for \(x\) and finding the corresponding values for \(y\).
When \(x = -2\), \(y = (-2)^3 - 3 = -8 - 3 = -11\). So, one point on the graph is (-2, -11).
When \(x = -1\), \(y = (-1)^3 - 3 = -1 - 3 = -4\). So, another point on the graph is (-1, -4).
When \(x = 0\), \(y = (0)^3 - 3 = 0 - 3 = -3\). So, another point on the graph is (0, -3).
When \(x = 1\), \(y = (1)^3 - 3 = 1 - 3 = -2\). So, another point on the graph is (1, -2).
When \(x = 2\), \(y = (2)^3 - 3 = 8 - 3 = 5\). So, another point on the graph is (2, 5).
Now, we can plot these points and connect them to form the graph.
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & -11 \\
-1 & -4 \\
0 & -3 \\
1 & -2 \\
2 & 5 \\
\hline
\end{array}
\]
The graph of the equation \(y = x^3 - 3\) is a curve that passes through these points.