document.write( "Question 1002513: a.) Find the slant asymptote of the graph of the rational function b use the slant asymptote to graph the rational function. f(x)=x^2+x-30/x-7.\r
\n" ); document.write( "\n" ); document.write( "a.)Find the slant asymptote graph of f
\n" ); document.write( "b.)use the slant asymptote to graph the rational function. First determine the symmetry of the graph f.
\n" ); document.write( " 1.)Find the y-intercept(s)
\n" ); document.write( " 2.)Find the x-intercepts
\n" ); document.write( " 3.)find the vertical asymptotes
\n" ); document.write( " 4.)find the horizontal asymptote\r
\n" ); document.write( "\n" ); document.write( "Plot points between and beyond each x-intercept and vertical asymptote, then use the information above to graph the rational functional. \n" ); document.write( "

Algebra.Com's Answer #619392 by josgarithmetic(39617) $\"\"$ $\"About$

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Written correctly, you are asking for f(x)=(x^2+x-30)/(x-7).
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document.write( "Synthetic Division as if checking root of 7\r\n" );
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document.write( "7     |    1      1     -30 \r\n" );
document.write( "      |           7     56\r\n" );
document.write( "      |_____________________________________\r\n" );
document.write( "          1       8     26     \r\n" );
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\n" ); document.write( "The quotient line means $\"x%2B8%2B26%2F%28x-7%29\"$ . The rational part approaches 0 as x goes unbounded, so the slant asymtptote is $\"highlight%28y=x%2B8%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Try to factorize the function.
\n" ); document.write( " $\"%28%28x-5%29%28x%2B6%29%29%2F%28x-7%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Let x=0 to find y axis intercept.
\n" ); document.write( " $\"y=%280-5%29%280%2B6%29%2F%280-7%29\"$
\n" ); document.write( " $\"highlight%28y=30%2F7%29\"$ -------y-intercept.\r
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\n" ); document.write( "\n" ); document.write( "Look at the numerator factors for the x-intercepts.
\n" ); document.write( "They are (5,0) and (-6,0).\r
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\n" ); document.write( "\n" ); document.write( "Vertical asymptote is where f is undefined:
\n" ); document.write( " $\"highlight%28x=7%29\"$ -----vertical asymptote\r
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\n" ); document.write( "\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C35%2C-10%2C35%2C%28x%5E2%2Bx-30%29%2F%28x-7%29%29\"$ \n" ); document.write( "

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