[-/1 Points] DETAILS MY NOTES TGEIALG5 5.4.0 Construct a table of solutions and then choose the graph of the equatic \[ y=x^{3}-1 \]

To construct a table of solutions for the equation \( y = x^3 - 1 \), we can choose a range of \( x \) values, calculate the corresponding \( y \) values, and then summarize the results in a table. ### Table of Solutions | \( x \) | \( y = x^3 - 1 \) | |---------|-------------------| | -2 | \( (-2)^3 - 1 = -8 - 1 = -9 \) | | -1 | \( (-1)^3 - 1 = -1 - 1 = -2 \) | | 0 | \( 0^3 - 1 = 0 - 1 = -1 \) | | 1 | \( 1^3 - 1 = 1 - 1 = 0 \) | | 2 | \( 2^3 - 1 = 8 - 1 = 7 \) | ### Summary of Solutions - For \( x = -2 \), \( y = -9 \) - For \( x = -1 \), \( y = -2 \) - For \( x = 0 \), \( y = -1 \) - For \( x = 1 \), \( y = 0 \) - For \( x = 2 \), \( y = 7 \) ### Graphing the Equation To graph the equation \( y = x^3 - 1 \), you would plot the points from the table above on a coordinate plane. The graph of this cubic function will have the following characteristics: - It will pass through the points listed in the table. - The graph will be continuous and smooth, with a characteristic "S" shape. - The function will have one real root at \( x = 1 \) (where \( y = 0 \)) and will extend to \( -\infty \) as \( x \) approaches \( -\infty \) and to \( +\infty \) as \( x \) approaches \( +\infty \). If you have graphing software or a graphing calculator, you can input the function \( y = x^3 - 1 \) to visualize the graph.