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4.6: Piecewise-defined Functions

Last updated

Oct 6, 2021
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- 4.5: Toolbox Functions
- 4.7: Composite functions

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In certain situations a numerical relationship may follow one pattern of behavior for a while and then exhibit a different kind of behavior. In a situation such as this, it is helpful to use what is known as a piecewise defined function - a function that is defined in pieces.
$clipboard_e5fb448f0dcdee1fda4bfad1acfd51b32.png$
In the above example of a piecewise defined function, we see that the $y$ values for the negative values of $x$ are defined differently than the $y$ values for the positive values of $x$
$clipboard_ea68efb190d5e7d001f6d761a3b94ccf2.png$
Sometimes we are given a graph and need to write a piecewise description of the function it describes.
$clipboard_ed03fecdd1995fec456e9d276b42f4562.png$
The piecewise function pictured above could be described as follows:
$clipboard_e491187c5095500bd1f0a3101eb309f79.png$
Exercises 4.6
Sketch a graph for each of the piecewise functions described below.
$clipboard_e026354e6745991244669d813b61d6e7f.png$
$clipboard_e6799170f4de896a07490ad8c0b53876f.png$
$clipboard_efbd2ed0098530b106cc993fe27cfbd7d.png$
$clipboard_ee0ef787c05c14525afdb48be0573c280.png$
$clipboard_e46b417d8a312b5c6913d6fe0a7df80c9.png$
$clipboard_e200f730d86dd22284bf4859b84a1f477.png$
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$clipboard_eba934cc8a9cc432b1b8ae848e62955d2.png$
$clipboard_e88c7521633e80c00fe26e624660867af.png$
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$clipboard_e0da0037a750d774aaeeaa31b3d82d3de.png$

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