function transformations

af(x)

vertical stretch or compression

bf(x) or f(bx)

horizontal stretch or compression

f(-x)

horizontal reflection across y axis

-f(x)

vertical reflection across x axis

f(x) + k

vertical translation up k units

f(x) - k

vertical translation down k units

f(x-h)

horizontal movement right h values

f(x+h)

horizontal movement left h values

af(x) affects the…

range

f(bx) affects the…

domain

f(-x) affects the…

domain

-f(x) affects the…

range

f(x) + k affects the…

range

f(x) - k affects the…

range

f(x-h) affects the…

range

f(x+h) affects the…

range

a>1

vertical stretch

a<1

vertical compression

b<1

horizontal stretch

b>1

horizontal compression (widen)

f(x) = x, linear function

d: all real numbers

r: all real numbers

f(x) = |x|, absolute value

d: all real numbers

r: [0, infinity)

f(x) = x², quadratic function

d: all real numbers

r: [0, infinity)