To find the table that represents \( y = f(-x) \), we need to reflect the original function \( y = f(x) \) across the y-axis. This means that for every positive x-value in the original function, we will find the corresponding value at the negative of that x-value in the new function.
Let's assume the original function \( f(x) \) has the following points based on the descriptions:
- \( f(1) = 2 \)
- \( f(2) = 0 \)
- \( f(3) = 2 \)
For \( f(-x) \), we look for:
- \( f(-1) = f(1) = 2 \)
- \( f(-2) = f(2) = 0 \)
- \( f(-3) = f(3) = 2 \)
Based on this logic, the corresponding values for \( y = f(-x) \) would be:
- When \( x = -1 \), \( f(-(-1)) = f(1) = 2 \)
- When \( x = -2 \), \( f(-(-2)) = f(2) = 0 \)
- When \( x = -3 \), \( f(-(-3)) = f(3) = 2 \)
Now, let's evaluate the provided options:
- The correct table for \( y = f(-x) \) should show:
- \( x = -1 \), \( f(-x) = 2 \)
- \( x = -2 \), \( f(-x) = 0 \)
- \( x = -3 \), \( f(-x) = 2 \)
Based on this evaluation, the correct response is:
x f(−x) -1 2 -2 0 -3 2
So, the correct answer is:
- \( x f(−x) \)
- -1 2
- -2 0
- -3 2