What is the transformation represented by y = f(-x)?

The transformation represented by the equation ( y = f(-x) ) indicates that for every input ( x ) in the function ( f ), the output is taken from the same value of the function at the negative input, ( -x ). This effectively flips the graph of the function over the y-axis, resulting in a reflection.

For example, if a point on the graph of ( f(x) ) is ( (a, b) ), then under the transformation ( y = f(-x) ), the new point will be ( (-a, b) ). Thus, any positive x-coordinate becomes its corresponding negative, creating the reflection characteristic associated with this transformation.

This concept establishes that the reflection occurs across the y-axis, as each point's horizontal position is reversed, while the vertical position remains unchanged. Consequently, understanding this transformation helps visualize how functions behave with respect to changes in their input, particularly regarding symmetry and reflection properties.