Question 1188026
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Write an equation for a rational function with:<br>
(1) Vertical asymptotes at x = -1 and x = 3: factors of (x+1) and (x-3) in the denominator<br>
(2) x-intercepts at x = -5 and x = -4: factors of (x+5) and (x+4) in the numerator<br>
(3) y-intercept at 7: f(0)=7<br>
The function is of the form<br>
{{{f(x)=(a(x+5)(x+4))/((x+1)(x-3))}}}<br>
Finish finding the function by knowing f(0)=7:<br>
{{{(a(5)(4))/((1)(-3))=7}}}
{{{20a/-3=7}}}
{{{20a=-21}}}
{{{a=-21/20}}}<br>
The function is<br>
{{{f(x)=((-21/20)(x+5)(x+4))/((x+1)(x-3))}}}<br>