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

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) |

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 |

Left h units, down k units | y = |x + h| - k | f(x) = f(x + h) - k |

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) |

(Right h units, up k units), (Reflection) and (Stretch or Shrink) | y = -a|x - h| + k | f(x) = -af(x - h) + k |