Use the image to answer the question.

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.