2.5

vertical functions

outside

horizontal functions

inside

horizontal shift to the left

y=f(x+h)

vertical shift up

y=f(x) +k

vertical compression

y=af(x) o<a<1

horizontal compression

y = af(x); a>1

reflect about the x axis

y=-f(x)

horizontal shift to the right

y=f(x-h)

vertical shift down

y=f(x)-k

vertical stretch

y = af(x); a>1

horizontal stretch

y = (1/ax); 0 < 1/a < 1

reflect about the y-axis

y=f(-x)

linear function

y=x

square function

y=x^2

cube function

y=x^3

square root function

y=√x

cube root function

y=³√x

reciprocal function

y = 1/x

absolute value function

y=|x|

constant function

y=b