If the function is f(x)=x3

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 \( f(-x) \).

Given that \( f(x) = x^3 \), we have:

\[ f(-x) = (-x)^3 = -x^3 \]

Now we can compute \( f(-x) \) for the given values of \( x \):

1. For \( x = 0 \): \[ f(0) = -0^3 = 0 \]

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

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

Now we can complete the table for \( f(-x) \):

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

So, the completed table is:

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