document.write( "Question 1146024: Write an equation for a rational function with:
\n" ); document.write( "Vertical asymptotes at x = 3 and x = -1
\n" ); document.write( "x intercepts at x = -4 and x = -6
\n" ); document.write( "y intercept at 9 \n" ); document.write( "

Algebra.Com's Answer #767304 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "(1) vertical asymptotes at x=3 and x=-1 --> factors of (x-3) and (x+1) in the denominator
\n" ); document.write( "(2) x intercepts at x=-4 and x=-6 --> factors of (x+4) and (x+6) in the numerator

\n" ); document.write( "So the function is of the form

\n" ); document.write( " $\"%28a%28x%2B4%29%28x%2B6%29%29%2F%28%28x-3%29%28x%2B1%29%29\"$

\n" ); document.write( "(3) y intercept at 9 (i.e., (0,9) is a point on the graph) --> to complete the function, evaluate the function at x=0 to solve for the value of the constant a.

\n" ); document.write( " $\"a%284%2A6%29%2F%283%2A%28-1%29%29+=+9\"$
\n" ); document.write( " $\"24a%2F-3+=+9\"$
\n" ); document.write( " $\"-8a+=+9\"$
\n" ); document.write( " $\"a+=+-9%2F8\"$

\n" ); document.write( "The function is

\n" ); document.write( " $\"%28%28-9%2F8%29%28x%2B4%29%28x%2B6%29%29%2F%28%28x-3%29%28x%2B1%29%29\"$
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