To determine which table shows that \( y = -f(x) \) results in a reflection over the x-axis, we need to check whether the values of \( -f(x) \) are the negatives of the corresponding values of \( f(x) \).
In the context of the tables you provided, we need to find values for \( f(x) \) and then see if the corresponding values of \( -f(x) \) are indeed the negatives of those.
Let's evaluate one of the options:
Option:
- \( x: 2, 0, 3, 6 \)
- \( f(x): 2, 0, 3, 6 \)
- \( -f(x): -2, 0, -3, -6 \)
This option gives:
- When \( x = 2 \), \( f(2) = 2 \) and \( -f(2) = -2 \).
- When \( x = 0 \), \( f(0) = 0 \) and \( -f(0) = 0 \).
- When \( x = 3 \), \( f(3) = 3 \) and \( -f(3) = -3 \).
- When \( x = 6 \), \( f(6) = 6 \) and \( -f(6) = -6 \).
Each value of \( -f(x) \) is indeed the negative of \( f(x) \), confirming that there is a reflection over the x-axis.
Thus, this table shows that \( y = -f(x) \) results in a reflection over the x-axis.
The correct answer is:
- \( x: 2, 0, 3, 6 \ f(x): 2, 0, 3, 6 \ -f(x): -2, 0, -3, -6 \)