Question 1178199
<br>
Vertical asymptotes at x = −4 and x = −2:<br>
Factors of (x+4) and (x+2) in the denominator<br>
x intercepts at (−6,0) and (−3,0):<br>
Factors of (x+6) and (x+3) in the numerator<br>
So the equation is of the form<br>
{{{(a(x+6)(x+3))/((x+4)(x+2))}}}
y intercept at (0,3):<br>
Solve f(0)=3 to find the constant factor a<br>
{{{(a(6)(3))/((4)(2)) = 3}}}
{{{18a/8 = 3}}}
{{{18a = 24}}}
{{{a = 24/18 = 4/3}}}<br>
ANSWER: {{{((4/3)(x+6)(x+3))/((x+4)(x+2))}}}<br>
{{{graph(400,400,-6,2,-10,10,((4/3)(x+6)(x+3))/((x+4)(x+2)))}}}<br>