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Graphing Absolute-Value Functions (page 1 of 2)

Taking the absolute value of a negative number makes it positive. For this reason, graphs of absolute value functions tend not to look quite like the graphs of linear functions that you've already studied. Because of how absolute values behave, it is important to include negative inputs in your T-chart when graphing absolute-value functions. If you do not pick x-values that will put negatives inside the absolute value, you will usually mislead yourself as to what the graph looks like.

For instance, suppose your class is taking the following quiz:

  • Graph y = | x + 2 |
  • One of the other students does what is commonly done: he picks only positive x-values for his T-chart:

      poor T-chart

    Then he plots his points:

      misleading plot

    These points are fine, as far as they go, but they aren't enough; they don't give an accurate idea of what the graph should look like. So the student then draws an erroneous graph:


    He just flunked the quiz. But you're more careful; you pick x-values that put a negative inside the absolute value, and you choose quite a few more points:

      better T-chart

    Then you plot your points:   Copyright Elizabeth Stapel 2000-2011 All Rights Reserved

      better plot

    ...and finally you connect your dots:

      y = | x + 2 |

    You have the correct graph:

      Right answer!
      y = | x + 2 |

    ...and you just passed the quiz!

While absolute-value graphs tend to look like the one above, with an "elbow" in the middle, this is not always the case. However, if you see a graph with an elbow like this, you should expect that the equation is probably an absolute value. In all cases, you should take care that you pick a good range of x-values; three x-values right next to each other will almost certainly not give you anywhere near enough information to draw a valid picture.

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Cite this article as:

Stapel, Elizabeth. "Graphing Absolute-Value Functions." Purplemath. Available from Accessed


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