5.1: Piecewise-defined 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.
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