a. Complete the table of values for the function y equals x cubed minus 2.

Question

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:

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