What does the notation f(-x) signify for the graph of f(x)?

The notation f(-x) indicates a reflection of the graph of the function f(x) across the y-axis. This transformation occurs because replacing x with -x effectively mirrors the points of the graph over the vertical axis. For any point (a, f(a)) on the original graph, the corresponding point on the transformed graph will be (-a, f(a)), which confirms this symmetry and reflection about the y-axis.

This principle is a fundamental aspect of transformations in function graphing and is essential for understanding the behavior of various functions when manipulated. Thus, when reviewing the graph of f(x), the new graph representing f(-x) will display all the corresponding points inverted along the y-axis, revealing this characteristic reflection.