To determine which option represents the graph of \( -f(x) \), we need to understand that graphing \( -f(x) \) flips the graph of \( f(x) \) over the x-axis. This means that all points (x, y) on the graph of \( f(x) \) will be transformed to (x, -y) on the graph of \( -f(x) \).
Without seeing the specific graphs provided, you would look for a graph that appears to be the mirror image of the original graph, but reflected across the x-axis.
If the original graph \( f(x) \) has peaks ( maxima) that appear above the x-axis, those peaks in \( -f(x) \) would appear below the x-axis, and vice versa for troughs (minima).
From the options provided:
- If option 4 looks like a reflected version of the original graph across the x-axis, then that would be the correct choice.
- Similarly, look at options 1, 2, and 3 and see if any resemble this vertical flip of the original wave pattern.
Select the option that reflects this flipping characteristic. Based on your description, make your selection accordingly.
1 answer