Andromeda
Note

Graph Reflecting

Definition

Graph reflecting is a transformation that produces a mirror image of a graph across a specified axis by negating its input or output values.

Why It Matters

Reflecting changes the “handedness” or parity of a graph. It is essential in physics and modeling for handling directional reversals, such as changing coordinate systems or modeling opposing forces.

Core Concepts

  • Vertical Reflection: y=f(x)y = -f(x)
    • How to read: “The value negative f of x.”
    • Meaning: Negate outputs, which flips the graph vertically across the xx-axis.
  • Horizontal Reflection: y=f(x)y = f(-x)
    • How to read: “The function f of negative x.”
    • Meaning: Negate inputs, which flips the graph horizontally across the yy-axis.
  • Symmetry Connection: A function is “even” if its horizontal reflection maps onto itself, and “odd” if its horizontal reflection equals its vertical reflection.

Connected Concepts