Transformations + Parent functions

y = f(x)

parent

y = f(x) + c

up c times

y = f(x) - c

down c times

y = f(x - c)

to the right c times

y = f(x + c)

to the left c times

y = -f(x)

reflection over the x-axis

y = f(-x)

reflection over the y-axis

y = c f(x), if |c| > 1

vertical stretch

y = c f(x), if 0 < |c| < 1

vertical shrink

y = f(cx), if |c|>1

horizontal shrink

y = f(cx), if 0 < |c| < 1

horizontal stretch

constant function

linear function

quadratic function

cubic function

absolute value function

radical/square root function

rational function