Question 1197127
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Write an equation for a rational function with
vertical asymptotes at x=-5 and x=6
x intercepts at x=2 and x=-2
y intercept at 7
y= 
~~~~~~~~~~~~~~


<pre>
Obviously, this rational function must have the binomial factors (x+5) and (x-6)
in the denominator and binomial factors (x-2) and (x+2) in the numerator.


So, we write  

    y = {{{(a*(x-2)*(x+2))/((x+5)*(x-6))}}} = {{{(a*(x^2-4))/(((x+5)*(x-6)))}}}.      (1)


Real coefficient "a" in the formula is intended to provide the necessary value y= 7 at x= 0.


To find "a", we equate function (1) to 7 at x= 0

    7 = {{{(a*(0^2-4))/((0+5)*(0-6))}}} = {{{(a*(-4))/(-30)}}} = {{{(2a)/15}}}.


From this equation, we find 

    a = {{{(7*15)/2}}} = {{{105/2}}}.


So, finally our function is

    y = {{{(105/2)*((x^2-4)/((x+5)*(x-6)))}}}.
</pre>

Solved.