SOLUTION: How dou you find the domain and their vertical, horizontal or oblique asymptote? r(x) = x^2+x-72/ x^2-x-56

Question 890057: How dou you find the domain and their vertical, horizontal or oblique asymptote?
r(x) = x^2+x-72/ x^2-x-56
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
r(x) = x^2+x-72/ x^2-x-56
The correct text form you want is r(x)=(x^2+x-72)/(x^2-x-56)
and as rendered looks like

Factor if you can.
.
A discontinuity occurs at x=8. This is because of the factor .
A vertical asymptote will occur at x=-7 because the function is undefined there.

Domain: U U .

The graph will not display properly the discontinuity at x=8 but it is there. The HORIZONTAL asymptote is y=1. This might be easier to understand if you take your original function before factoring and examine what happens for x extremely large or small without bound. The x^2 terms in numerator and denominator become increasingly far more important, so each approaches the same square value, and you have the ratio of these.
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