Graphing Functions

General Mathematics — Second Secondary

Geometric transformations

Comparison aspect	Main idea	Keywords
f(x) + a	vertical translation up by a when a > 0 and down when a < 0	verticaltranslationdown
f(x + a)	horizontal translation to the left by a when a > 0 and to the right when a < 0. The sign inside the bracket reverses the direction you might expect	horizontaltranslationleftright
k · f(x)	vertical stretch by factor k when k > 1 or vertical compression when 0 < k < 1	verticalstretchfactorcompression
f(−x)	reflection in the y-axis	reflectionaxis
−f(x)	reflection in the x-axis	reflectionaxis
When several transformations are applied, work in this order	the changes inside the bracket (horizontal translation and reflection in the y-axis) then the stretch or reflection in the x-axis then the final vertical translation	changesinsidebrackethorizontal

Graphing Functions · 2 / 5