Graph Translations

the graph translationa and what they do to the co-ordinates GCSE maths

f(x) + d

vertical translation up d units
(x,y) -> (x,y+d)

f(x) - d

vertical translation down d units
(x,y) -> (x,y-d)

f(x+c)

horizontal translation left c units
(x,y) -> (x-c,y)

f(x-c)

horizontal translation right c units
(x,y) -> (x+c,y)

-f(x)

reflection over x axis
(x,y) -> (x,-y)

f(-x)

reflection over y axis
(x,y) -> (-x,y)