What transformation occurs when a function is evaluated at -x?

When a function is evaluated at -x, the transformation that occurs is a reflection across the y-axis. This means that for any point (x, f(x)) on the graph of the function, the corresponding point (-x, f(-x)) will be present on the graph as well. This reflection effectively flips the graph of the function over the y-axis, resulting in the same output for the negative input as would have been obtained from the positive input, thus mirroring the function's behavior on either side of the y-axis.

For instance, if you take a simple function like f(x) = x², evaluating it at -x would yield f(-x) = (-x)² = x², which maintains the same shape but showcases the reflection property. This transformation preserves the distances and angles but alters the positioning relative to the y-axis.

Understanding this concept is important in analyzing how function graphs behave under different transformations, especially when relating to symmetry.