Question

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

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

Answer 1

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:

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