document.write( "Question 739552: How do i know how to graph this equation:
\n" ); document.write( "f(x)= { 2x-1 -2 \n" ); document.write( " 3-x 1 \n" ); document.write( "

Algebra.Com's Answer #451196 by KMST(5328) $\"\"$ $\"About$

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There is a typo somewhere in your piecewise function.
\n" ); document.write( " $\"f%28x%29=2x-1\"$ for $\"-2%3C=x%3C=1\"$ means
\n" ); document.write( " $\"f%28-2%29=2%2A%28-2%29-1=-4-1=-5\"$ and
\n" ); document.write( " $\"f%281%29=2%2A%281%29-1=2-1=1\"$
\n" ); document.write( "The other piece of the function, defined as
\n" ); document.write( " $\"f%28x%29=3-x\"$ for $\"1%3C=x%3C=4\"$ would mean
\n" ); document.write( " $\"f%284%29=3-4=-1\"$ and
\n" ); document.write( " $\"f%281%29=3-1=2\"$
\n" ); document.write( "The problem is that as written, we would have
\n" ); document.write( " $\"f%281%29=1\"$ for one piece and $\"f%281%29=2\"$ for the other piece, and that cannot be.
\n" ); document.write( "A function cannot be defined in such a way that two different $\"y=f%28x%29\"$ values correspond to the same $\"x\"$ value.
\n" ); document.write( "Unless the typo is somewhere else, one of the pieces of the function has to let go of $\"x=1\"$
\n" ); document.write( "
\n" ); document.write( "The graph of
\n" ); document.write( " $\"f%28x%29=%28matrix%282%2C3%2C2x-1%2Cfor%2C-2%3C=x%3C=1%2C3-x%2Cfor%2C1%3Cx%3C=4%29%29\"$ is

The points (-2,-5), (1,1), and (4,-1) are part of the function and are shown as solid points in the graph.
\n" ); document.write( "The point (1,2) is not part of the function and is drawn as an unfilled circle to show that is not part of the graph.
\n" ); document.write( "The line segment connecting (-2,-5) and (1,1) and both of its ends are the graph of $\"f%28x%29=2x-1\"$ for $\"-2%3C=x%3C=1\"$
\n" ); document.write( "The line segment connecting (1,2) and (4,-1), along with point (4,-1) are the graph of $\"f%28x%29=3-x\"$ for $\"1%3Cx%3C=4\"$ \n" ); document.write( "

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