Question

for the equation $y = x^3 + 1$, (a) create a table with ordered pairs that are solutions of the equation, and (b) graph the equation. (a) complete the following table of ordered pairs that are solutions of the equation. \

$$\begin{tabular}{|c|c|} \\hline $\\boldsymbol{x}$ & $\\boldsymbol{y}$ \\\\ \\hline $-1$ & $\\square$ \\\\ \\hline $0$ & $\\square$ \\\\ \\hline $1$ & $\\square$ \\\\ \\hline $2$ & $\\square$ \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Find y when x = -1

Substitute \( x = -1 \) into \( y = x^3 + 1 \).
\( y = (-1)^3 + 1 = -1 + 1 = 0 \)

Step2: Find y when x = 0

Substitute \( x = 0 \) into \( y = x^3 + 1 \).
\( y = 0^3 + 1 = 0 + 1 = 1 \)

Step3: Find y when x = 1

Substitute \( x = 1 \) into \( y = x^3 + 1 \).
\( y = 1^3 + 1 = 1 + 1 = 2 \)

Step4: Find y when x = 2

Substitute \( x = 2 \) into \( y = x^3 + 1 \).
\( y = 2^3 + 1 = 8 + 1 = 9 \)

Answer:

For \( x = -1 \), \( y = 0 \);
For \( x = 0 \), \( y = 1 \);
For \( x = 1 \), \( y = 2 \);
For \( x = 2 \), \( y = 9 \).

The completed table is:

x	y
0	1
1	2
2	9