To determine the values of \( f(-x) \) based on the original graph \( y = f(x) \), we need to reflect the graph across the \( y \)-axis. This means that for every point \( (a, b) \) on the graph of \( f(x) \), the corresponding point \( (-a, b) \) will be on the graph of \( f(-x) \).
Since I can't see the graph directly, I'll provide you with the general approach to find \( f(-x) \):
- Look at the original function's values for some positive \( x \) values.
- Note the corresponding \( y \) values.
- Take these \( x \) values and switch their sign.
- The \( y \) values will remain the same because the graph is being mirrored over the \( y \)-axis.
Once you have the negative \( x \) values, look for the table that correctly reflects these pairs.
For example, if the original function is:
- \( f(1) = 2 \)
- \( f(2) = 0 \)
- \( f(3) = 2 \)
Then \( f(-1) = 2 \), \( f(-2) = 0 \), and \( f(-3) = 2 \).
Using this method, check which of the response tables matches the calculated \( f(-x) \) values.
Based on common patterns:
- For every positive input in \( f(x) \), the output will remain unchanged in \( f(-x) \).
- Conversely, for every negative input in \( f(x) \), you will need to find the corresponding positive input's output.
Select the table that matches your findings from the above logic!
1 answer