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