document.write( "Question 152606: write |x| as a piecewise function. \n" ); document.write( "

Algebra.Com's Answer #112168 by mducky2(62) $\"\"$ $\"About$

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Let's write |x| as a function:
\n" ); document.write( "f(x) = |x|
\n" ); document.write( "
Let's solve for f(x) when x > 0. We know that for all x > 0, the absolute value doesn't change anything, since x is already positive. Therefore:
\n" ); document.write( "For x > 0, f(x) = x
\n" ); document.write( "
We also know that for all x < 0, the absolute value makes the negative number positive again. Multiplying the negative number x with -1 has the same effect, so:
\n" ); document.write( "For x < 0, f(x) = -x
\n" ); document.write( "
Now we need to know f(x) when x = 0.
\n" ); document.write( "f(x) = |0| = 0
\n" ); document.write( "The number didn't change. Therefore:
\n" ); document.write( "For x = 0, f(x) = x
\n" ); document.write( "
Combining everything together:
\n" ); document.write( "The piecewise function of f(x) = |x| is
\n" ); document.write( "for x >= 0, f(x) = x
\n" ); document.write( "for x < 0, f(x) = -x \n" ); document.write( "

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