Reflections (Transformations): Mirrors
A reflection flips a graph like a mirror. The shape stays the same—only the direction changes.
Quick rules
Reflect over the y-axis: replace x with −x → y = f(−x) (points: (x, y) → (−x, y))
Reflect over the x-axis: make y negative → y = −f(x) (points: (x, y) → (x, −y))
Over both axes (through the origin): y = −f(−x) (points: (x, y) → (−x, −y))
Example with a parabola
Start with the base graph (dashed): f(x) = (x − 2)² / 4
Reflect over the y-axis (step-by-step)
1) Replace x with −x
y = ((−x) − 2)² / 4
2) Simplify: (−x − 2) = −(x + 2) → squaring removes the minus
y = (x + 2)² / 4
learn