document.write( "Question 454009: I need to create a rational function with the following:
\n" ); document.write( "Crosses x-axis at 2
\n" ); document.write( "Touches the x-axis at -1
\n" ); document.write( "One verticle asymptote at x=-5 and another at x=6
\n" ); document.write( "One horizontal asymptote at y=3\r
\n" ); document.write( "\n" ); document.write( "help! i need to know the steps \n" ); document.write( "

Algebra.Com's Answer #311823 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "If your function crosses the

-axis at 2, then the numerator polynomial must have a zero at 2. Hence, one factor of the numerator is

\r
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\n" ); document.write( "\n" ); document.write( "If your function just touches the

-axis at -1, then the numerator polynomial must have a zero at -1 with a multiplicity of 2. Hence, another factor of the numerator is

\r
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\n" ); document.write( "\n" ); document.write( "If the function must have a vertical asymptote at -5, then the denominator polynomial must have a zero at -5. Hence a factor of the denominator must be

.\r
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\n" ); document.write( "\n" ); document.write( "Likewise, for a vertical asymptote at 6, the denominator must have a factor of

.\r
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\n" ); document.write( "\n" ); document.write( "In order for there to be a horizontal asymptote other than the

-axis, the degree of the numerator and denominator polynomials must be the same and the ratio of the lead coefficients must be equal to the value of the

-coordinate of the ordered pairs in the asymptote.\r
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\n" ); document.write( "\n" ); document.write( "In order to accomplish equal degree, we need to double up on one of the factors in the denominator. I choose the

, hence the first factor fo the denominator becomes

\r
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\n" ); document.write( "\n" ); document.write( "In order for there to be a 3 to 1 ratio between the lead coefficients on the numerator and denominator such that the horizontal asymptote occurs at

, insert a factor of 3 into the numerator.\r
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\n" ); document.write( "\n" ); document.write( "Putting it all together:\r
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\r
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\n" ); document.write( "\n" ); document.write( "You can multiply the factors yourself if that is the form of the answer you are required to submit.\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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$\"The$

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