Question 1146024
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(1) vertical asymptotes at x=3 and x=-1  -->  factors of (x-3) and (x+1) in the denominator
(2) x intercepts at x=-4 and x=-6  -->  factors of (x+4) and (x+6) in the numerator<br>
So the function is of the form<br>
{{{(a(x+4)(x+6))/((x-3)(x+1))}}}<br>
(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.<br>
{{{a(4*6)/(3*(-1)) = 9}}}
{{{24a/-3 = 9}}}
{{{-8a = 9}}}
{{{a = -9/8}}}<br>
The function is<br>
{{{((-9/8)(x+4)(x+6))/((x-3)(x+1))}}}<br>