document.write( "Question 934457: Write a rational function g with vertical asymptotes at x=3, x=-3, a horizontal asymptote at y=-2 and with no x intercept. \n" ); document.write( "

Algebra.Com's Answer #567784 by MathLover1(20850) $\"\"$ $\"About$

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given: vertical asymptotes at $\"x=3\"$ , $\"x=-3\"$ , a horizontal asymptote at $\"y=-2\"$ and with no $\"x\"$ intercept:\r
\n" ); document.write( "\n" ); document.write( "Since $\"g\"$ has a vertical asymptotes at $\"x+=+3\"$ and $\"x+=+-3\"$ , then the denominator of the rational function contains the product of $\"%28x+-3%29\"$ and $\"%28x+%2B+3%29\"$ . Function $\"g\"$ has the form:\r
\n" ); document.write( "\n" ); document.write( " $\"g%28x%29+=+h%28x%29+%2F%28+%28x-3%29%28x+%2B+3%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "For the horizontal asymptote to exist, the numerator of

. At the same time the numerator of $\"g%28x%29+has+%7B%7B%7Bno\"$ real zeros. \r
\n" ); document.write( "\n" ); document.write( "Hence\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+%28-2x%5E2+-6+%29+%2F+%28+%28x+-3%29%28x+%2B+3%29+%29\"$ \r
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