document.write( "Question 855986: Gragh each function. Indicate with coordinate labels all x-interceptions, y-interceptions, maxima and minima. Indicate with a dotted line and label all vertical, horizontal, and oblique asymptotes.
\n" ); document.write( "f(x)=(x^3-4x^2+x+6) / (x^2 -3x+2)\r
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Algebra.Com's Answer #515676 by josgarithmetic(39620) $\"\"$ $\"About$

You can put this solution on YOUR website!
This will help most of the way, useful in sketching a graph.\r
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\n" ); document.write( "\n" ); document.write( "Polynomial Division will show quotient of $\"x%2B1%2B%282x%2B4%29%2F%28x%5E2-3x%2B2%29\"$ , so a slant asymptote will be $\"highlight%28y=x%2B1%29\"$ , since the remainder, $\"%282x%2B4%29%2F%28x%5E2-3x%2B2%29\"$ will become increasingly smaller as x becomes unbounded.\r
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\n" ); document.write( "\n" ); document.write( "f(x) is factorable.
\n" ); document.write( " $\"highlight_green%28f%28x%29=%28%28x%2B1%29%28x-2%29%28x-3%29%29%2F%28%28x-1%29%28x-2%29%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Numerator factored indicates zeros at x=-1 and x=3.
\n" ); document.write( "Hole at x=2. (see common factor in numerator and denominator).
\n" ); document.write( "Vertical Asymptote at x=1 (see what this does to denominator).
\n" ); document.write( "Slant asymptote, y=x+1.
\n" ); document.write( "You can test for signs around critical points -1,1,2,3.\r
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\n" ); document.write( "\n" ); document.write( " $\"graph%28300%2C300%2C-3%2C6%2C-10%2C15%2C%28x%5E3-4x%5E2%2Bx%2B6%29%2F%28x%5E2-3x%2B2%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Not sure why the hole at x=2 does not appear as a hole, but that IS a hole, undefined function at x=2. \n" ); document.write( "

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