document.write( "Question 728570: create a rational function with a vertical asymptotes x=ą1 and oblique asymptote of y=2x-3 and y-intercept of 4 \n" ); document.write( "

Algebra.Com's Answer #445644 by KMST(5347) $\"\"$ $\"About$

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$\"y=2x-3%2B7%2F%28x%5E2-1%29=%282x%5E3-3x%5E2-2x-4%29%2F%28x%5E2-1%29\"$ $\"graph%28300%2C300%2C-5%2C5%2C-15%2C10%2C2x-3%2C2x-3-7%2F%28x%5E2-1%29%29\"$
\n" ); document.write( "If we add to $\"y=2x-3\"$ a term $\"f%28x%29\"$ such that $\"lim%28+x-%3Einfinity%2C+f%28x%29+%29+=0\"$ ,
\n" ); document.write( "we get a function that has $\"y=2x-3\"$ for an asymptote.
\n" ); document.write( "Since we want $\"y=4\"$ for $\"x=0\"$ (y-intercept=4),
\n" ); document.write( "we need
\n" ); document.write( " $\"2%2A0-3%2Bf%280%29=4\"$ --> $\"-3%2Bf%280%29=4\"$ --> $\"f%280%29=4%2B3=7\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"g%28x%29=1%2F%28%28x%2B1%29%28x-1%29%29=1%2F%28x%5E2-1%29\"$ is a function with vertical asymptotes {x=-1}}} and $\"x=1\"$ and
\n" ); document.write( " $\"lim%28+x-%3Einfinity%2C1%2F%28x%5E2-1%29%29+=0\"$ .
\n" ); document.write( " $\"g%28x%29\"$ is promising, but $\"g%280%29=-1\"$ ,
\n" ); document.write( "so we use $\"f%28x%29=-7g%28x%29\"$ which makes $\"f%280%29=-7%2A%28-1%29=7\"$ . \n" ); document.write( "

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