maths - rules for transformations of linear functions

f(x+a)

shift left

f(x-a)

shift right

f(x)+a

shift up

f(x)-a

shift down

-f(x)

reflect across x-axis

f(-x)

reflect across y-axis

af(x), a>1

stretch vertically by a factor of a

af(x), 0<a<1

compress vertically by a factor of a

f(ax), a>1

compress horizontally by a factor of 1/a

f(ax), 0<a<1

stretch horizontally by a factor of 1/a