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

Recent Articles

  1. Additive Inverse of a Complex Number

    Sep 24, 21 03:39 AM

    What is the additive inverse of a complex number? Definition and examples

    Read More

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.