a. Complete the table of values for the function y equals x cubed minus 3.

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
​(Type integers or simplified fractions. Type N if the function is​ undefined.)

Answer 1

To complete the table of values for the function \( y = x^3 - 3 \), we will calculate \( y \) for the specified values of \( x \).

1. For \( x = -3 \): \[ y = (-3)^3 - 3 = -27 - 3 = -30 \]

2. For \( x = -2 \): \[ y = (-2)^3 - 3 = -8 - 3 = -11 \]

3. For \( x = -1 \): \[ y = (-1)^3 - 3 = -1 - 3 = -4 \]

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

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

6. For \( x = 2 \): \[ y = (2)^3 - 3 = 8 - 3 = 5 \]

7. For \( x = 3 \): \[ y = (3)^3 - 3 = 27 - 3 = 24 \]

Now we can summarize the completed table:

\[ \begin{array}{|c|c|} \hline x & y \ \hline -3 & -30 \ -2 & -11 \ -1 & -4 \ 0 & -3 \ 1 & -2 \ 2 & 5 \ 3 & 24 \ \hline \end{array} \]