the function is f(x)=x^3

Question

, complete the table for its horizontal reflection.(2 points)
x 0 1 2
f(−x)

Answer 1

To find the horizontal reflection of the function \( f(x) = x^3 \), we need to evaluate \( f(-x) \) for the values of \( x \) in the table.

1. Calculate \( f(-x) \) for given \( x \):

   • For \( x = 0 \): \[ f(-0) = (-0)^3 = 0 \]
   • For \( x = 1 \): \[ f(-1) = (-1)^3 = -1 \]
   • For \( x = 2 \): \[ f(-2) = (-2)^3 = -8 \]

2. Complete the table:

\[ \begin{array}{|c|c|c|} \hline x & f(-x) \ \hline 0 & 0 \ 1 & -1 \ 2 & -8 \ \hline \end{array} \]

So, the completed table for \( f(-x) \) is:

• For \( x = 0 \), \( f(-0) = 0 \)
• For \( x = 1 \), \( f(-1) = -1 \)
• For \( x = 2 \), \( f(-2) = -8 \)

The values are:

• \( f(-0) = 0 \)
• \( f(-1) = -1 \)
• \( f(-2) = -8 \)