document.write( "Question 904333: find the domain and range please show me how you would graph this.
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\n" ); document.write( "x+3 \n" ); document.write( "

Algebra.Com's Answer #548649 by KMST(5328) $\"\"$ $\"About$

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$\"f%28x%29=1%2F%28x%2B3%29\"$ does not exist when $\"x%2B3=0\"$ <---> $\"x=-3\"$ .
\n" ); document.write( "For any other value of $\"x\"$ , $\"f%28x%29=1%2F%28x%2B3%29\"$ can be calculated,
\n" ); document.write( "so the domain is all the real numbers except $\"-3\"$ .
\n" ); document.write( " $\"x=-3\"$ is the equation of the vertical asymptote.
\n" ); document.write( "For $\"x%3C-3\"$ , $\"x%2B3%3C0\"$ and $\"f%28x%29=1%2F%28x%2B3%29%3C0\"$ .
\n" ); document.write( "For $\"x%3E-3\"$ , $\"x%2B3%3E0\"$ and $\"f%28x%29=1%2F%28x%2B3%29%3E0\"$ .
\n" ); document.write( "As $\"x\"$ approaches $\"-3\"$ (from either side),
\n" ); document.write( " $\"abs%28x%2B3%29\"$ approaches zero, and $\"abs%28f%28x%29%29=abs%281%2F%28x%2B3%29%29=1%2Fabs%28x%2B3%29\"$ grows without bounds.
\n" ); document.write( "As $\"abs%28x%29\"$ increases, $\"abs%28f%28x%29%29=abs%281%2F%28x%2B3%29%29=1%2Fabs%28x%2B3%29\"$ approaches zero,
\n" ); document.write( "so $\"y=0\"$ is the horizontal asymptote.
\n" ); document.write( " $\"f%28x%29=1%2F%28x%2B3%29\"$ can take any value, except zero,
\n" ); document.write( "so its range is all the real numbers except zero.
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