What effect does f(|x|) have on the function's graph?

The correct answer explains how applying the absolute value function to the input ( |x| ) transforms the graph of ( f(x) ). When using ( f(|x|) ), all negative values of ( x ) are replaced with their positive counterparts, which effectively reflects the portion of the graph in the left half-plane (where ( x < 0 )) across the y-axis.

This means that any point on the graph where ( x ) was negative will now have a corresponding point on the graph where ( x ) is positive, creating a mirror effect. Therefore, the shapes and features of the graph for positive ( x ) are duplicated for negative ( x ), resulting in the graph being symmetric about the y-axis. This reflection across the y-axis gives rise to this specific interpretation of how the original function behaves when the input is transformed to ( |x| ).