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Graphing Absolute Values

Module by: Kenny M. Felder. E-mail the author

Summary: This module describes how to graph absolute values.

You can graph y=∣x∣y=∣x∣ size 12{y= lline x rline } {} easily enough by plotting points. The characteristic V shape is illustrated below, with a couple of sample points highlighted.

Figure 1: y = | x | y = | x |
Graph showing the absolute value of x.

Of course, this shape is subject to the same permutations as any other function! A few examples are given below.

Figure 2
(a) | x - 5 | + 1 | x - 5 | + 1 Moves right 5, up 1 (b) - | x | + 1 - | x | + 1 Flips over x x -axis, moves up 1 (c) 2 ⁢ | x + 5 | 2 ⁢ | x + 5 | 5 left, vertically stretched
Graph of the absolute value of x+5, the same as above but shifted to the left 5 units (x+5).Graph of the absolute value of -|x|+1, the same as first but vertically flipped and shifted up 1 unit.Graph of the absolute value of 2|x+5|, the same as first vertically stretched by a factor of 2 (skinnier).

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