## Function and Relation LibraryABSOLUTE VALUE FUNCTION -
A Basic Function Which Is the Composition of More Basic Functions y = |x| |

See Composition of Functions for a full discussion on composition of functions. The absolute value function serves as an example.

This function is also the composition of two other functions. If one squares a number, then takes its square root, the result is the absolute value. In algebraic symbols, (x²) = |x|.

x ^{ } |
x x ^{2} |
x ^{2}
(x^{2}) |

This sequence of functions of other functions is called composition of functions.

x^{ }
x^{2}
(x^{2})

In common precalc function notation it is written:

- Let f(x) = x
^{2}. - Let g(x) = (x)
- State g(f(x)) or (g o f)(x).
- In other words: Find
(x
^{2})For negative numbers, the slope of the absolute value function is -1.

For positive numbers, the slope of the absolute value function is 1.

The absolute value function has no slope at zero.

The absolute value is used to force the results to be positive. The squaring then square rooting technique is used in computing standard deviations and in computing the distance between two points. Each of these requires addition of the squared numbers.

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**Exploring Functions Throught the Use of Manipulatives**(ISBN: 0-9623593-3-5).You are hereby granted permission to make ONE printed copy of this page and its picture(s) for your PERSONAL and not-for-profit use. YOU MAY NOT MAKE ANY ADDITIONAL COPIES OF THIS PAGE, ITS PICTURE(S), ITS SOUND CLIP(S), OR ITS ANIMATED GIFS WITHOUT PERMISSION.

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