Stretches and Compressions

Hello everyone, this is Steven. Today we learned about Stretches and Compressions.

Stretches and Compressions Rules:

Vertical Stretches and Compressions

We say that given f(x), a<0

y=af(x) - stretches the graph vertically by a factor of "a" units

y=1/a f(x) - compresses the graph vertically by a factor of "a" units

We call "a" a vertical stretch/compression. Notice that the coordinates of the points (x,y) translate to (x, ay) or (x, 1/a y). The value of x does not change.

Horizontal Stretches and Compressions

We say that given f(x), b>0

y=f(bx) - Compresses the entire graph horizontally by a factor of "b" units.

y=f(1/b x) - Stretches the entire graph horizontally by a factor of "b" units.

We call "b" a horizontal stretch/compression. Notice that the coordinates of the points (x,y) translate to (bx,y) or (1/b x,y). The value of y does not change.