Transformation rules for functions

Function Notation Type of Transformation Change to Coordinate Point f(x) + d Vertical translation up d units (x, y) 9 (x, y + d) f(x) — d Vertical translation down d units (x, y) 9 (x, y — d) f(x 4- c) Horizontal translation left c units (x, y) 9 (x — c, y) f(x - c) Horizontal translation right c units (x, y) 9 (x + c, y) —f(x) Reflection over x»axis (x, y) 9 (x, —y) f(—x) Reflection overy—axis (x, y) 9 (—x, y) Vertical stretch for |a |> 1 ale) _ . (X, Y) 9 (X, av) Vertlcal compresslon for 0 < |a| < 1 Horizontal compression for |b| > 1 f(bx) (£109 Horizontal stretch forO < |b| < 1