Question

a. Complete the table of values for the function y equals x cubed minus 2.
x
y
minus3
  
enter your response here
minus2
  
enter your response here
minus1
  
enter your response here
0
  
enter your response here
1
  
enter your response here
2
  
enter your response here
3
  
enter your response here

Answer 1

To complete the table of values for the function \( y = x^3 - 2 \), we need to substitute each value of \( x \) into the equation and calculate \( y \).

Here are the calculations for each \( x \):

1. For \( x = -3 \):
\[
y = (-3)^3 - 2 = -27 - 2 = -29
\]

2. For \( x = -2 \):
\[
y = (-2)^3 - 2 = -8 - 2 = -10
\]

3. For \( x = -1 \):
\[
y = (-1)^3 - 2 = -1 - 2 = -3
\]

4. For \( x = 0 \):
\[
y = (0)^3 - 2 = 0 - 2 = -2
\]

5. For \( x = 1 \):
\[
y = (1)^3 - 2 = 1 - 2 = -1
\]

6. For \( x = 2 \):
\[
y = (2)^3 - 2 = 8 - 2 = 6
\]

7. For \( x = 3 \):
\[
y = (3)^3 - 2 = 27 - 2 = 25
\]

Now we can fill in the table:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-3 & -29 \\
-2 & -10 \\
-1 & -3 \\
0 & -2 \\
1 & -1 \\
2 & 6 \\
3 & 25 \\
\hline
\end{array}
\]