# 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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