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Function Transformations

Algebra IISophomoreUpdated October 25, 2026

Rules for vertical, horizontal, and reflection transformations of functions.

Function Transformations

Vertical Shift: changing k in y = f(x) + k moves line up (if positive) or down (if negative).

Horizontal Shift: changing h in y = f(x - h) moves line right (if positive) or left (if negative).

Reflection: negative sign in y = -f(x) reflects the graph across the x-axis.

Absolute Value Vertex Form: y = a|x - h| + k with vertex at (h, k) and slope factor a.

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