document.write( "Question 895387: Explain how to Find any horizontal and vertical asymptotes and any holes that may exist for the rational function. Draw a graph, including any x and y intercepts: \r
\n" ); document.write( "\n" ); document.write( "y=((x^2)+7x+12)/(x+4) \n" ); document.write( "

Algebra.Com's Answer #542779 by josgarithmetic(39620) $\"\"$ $\"About$

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That rational equation has no horizontal asymptotes. Notice x unbounded approaches either negative infinity or positive infinity, based on y approaching $\"x%5E2%2Fx\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Just to be more certain in possible vertical asymptotes, factorize the numerator if possible.
\n" ); document.write( "(x+3)(x+4)-----------the numerator.
\n" ); document.write( "NO vertical asymptote, because $\"y=%28%28x%2B3%29%28x%2B4%29%29%2F%28x%2B4%29\"$
\n" ); document.write( " $\"y=%28%28x%2B3%29cross%28%28x%2B4%29%29%29%2Fcross%28%28x%2B4%29%29\"$
\n" ); document.write( " $\"y=x%2B3\"$
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\n" ); document.write( "Your rational equation is the line but MISSING x=-4. There is no included point at x=-4. You can call this a hole in the line. (This cannot be seen well on most graphs produced through software, but you can represent what you want in a manually drawn graph or sketch.)\r
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\n" ); document.write( "\n" ); document.write( "No real use in looking for slant asymptote, since the rational equation is already a line (missing one point.) \n" ); document.write( "

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