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

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