Question

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

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