If the function is f (x) = x?, complete the table for its horizontal reflection.

x f(-x)
0 ?
1 ?
2 ?

1 answer

To find the values of the function \( f(-x) \) for the function \( f(x) = x^2 \), we need to calculate \( f(-x) \) for the corresponding \( x \) values.

Since the function is \( f(x) = x^2 \):

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

This indicates that the function \( f(-x) \) is the same as \( f(x) \) since \( x^2 \) is even.

Now we can complete the table:

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

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

  • For \( x = 2 \): \[ f(-2) = f(2) = 2^2 = 4 \]

Thus, the completed table is:

\[ \begin{array}{|c|c|} \hline x & f(-x) \ \hline 0 & 0 \ 1 & 1 \ 2 & 4 \ \hline \end{array} \]

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