Question 1200447
.
Write an equation for a rational function with:

Vertical asymptotes at x = -6 and x = 5

x intercepts at x = -4 and x = -3

Horizontal asymptote at y = 7
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<pre>
This rational function wants to have binomial factors (x+6) and (x-5)
in the denominator to provide the necessary asymptotes

and binomial factors (x+4) and (x+3) in the numerator to provide the necessary x-intercepts.


So, we write

    f(x) = {{{a*(((x+4)*(x+3))/((x+6)*(x-5)))}}}


with coefficient "a".


Horizontal asymptote y= 7 means that  { limit f(x) }  is 7 when x tends to +oo  or -oo,
which means that a= 7.


Finally, the function is  f(x) = {{{7*(((x+4)*(x+3))/((x+6)*(x-5)))}}}.    <U>ANSWER</U>
</pre>

Solved.


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Use free of charge online plotting tool at this web-site


www.desmos.com/calculator 


to plot the graph of the function and to see visually that the function has all necessary properties.