If the function is f(x)=x3

Question

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

To find the horizontal reflection of the function \( f(x) = x^3 \), we evaluate \( f(-x) \).

1. Substitute \(-x\) into the function: \[ f(-x) = (-x)^3 \]

2. Simplifying the expression: \[ (-x)^3 = -x^3 \]

So, we want to compute \( f(-x) \) for the given values of \( x \) in the table.

Table for \( f(-x) \):

• When \( x = 0 \): \[ f(-0) = -0^3 = 0 \]

• When \( x = 1 \): \[ f(-1) = -1^3 = -1 \]

• When \( x = 2 \): \[ f(-2) = -2^3 = -8 \]

Now, we can fill in the table:

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

Therefore, the completed table looks like this:

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