Absolute Value Graph

Absolute Value Graph

Author: Craig Coletta

This lesson will demonstrate how to graph the solution set of an absolute value equation.

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Absolute Value Graph




This is an example of the graph of an absolute value equation y=|x+2|.


Remember that the absolute value of a number can best be expressed as “the number of steps away from zero, in either a positive or negative direction, you must take in order to reach a number.


Thus, the absolute value of 2 is 2 – two steps away from zero.


The absolute value of -2 is ALSO 2 – two steps away from zero. An absolute value can therefore NEVER be a negative number.


The absolute value of negative 2 is written as |-2|, The bars on either side of the number illustrate that the absolute value of the number is being represented.


So imagine an equation like this:




In this example, no matter what value is plugged in for x, y can never be a negative number: if x is -3, the equation simplifies to:




giving the result:




Since the absolute value of -1 = 1, y=1


In this example, the lowest possible value of y is 0, and as the value of x moves further into negative numbers, the value of y will become larger and larger positive numbers. Thus the graph appears as an upward-pointing “V” shape with its vertex at 0 and positive or negative values of x producing larger and larger positive values for y..


An equation such as x=|y+2| would yield a rightward-pointing “V” shape (Try graphing this as an example.