The family of absolute value functions

This math lesson will show the family of absolute value functions using the parent absolute value function y = |x|

Vertical Translation
Parent function: Translation toward the right h units, h > 0: Translation toward the left h units, h > 0:	y = |x| y = |x - h| y = |x + h|	y = f(x) y = f(x - h) y = f(x + h)
Horizontal Translation
Parent function: Translation up k units, k > 0: Translation down k units, k > 0:	y = |x| y = |x| + k y = |x| - k	y = f(x) y = f(x) + k y = f(x) - k
Combined Translation
Left h units, down k units	y = |x + h| - k	f(x) = f(x + h) - k
Reflection, Stretch or Shrink
Parent function: Reflection in x-axis	y = |x| y = -|x|	y = f(x) y = -f(x)
Parent function: Stretch (a > 1) or shrink (0 < a < 1)	y = |x| y = a|x|	y = f(x) y = af(x)
Combined Transformation
(Right h units, up k units), (Reflection) and (Stretch or Shrink)	y = -a|x - h| + k	f(x) = -af(x - h) + k