SOLUTION: Give an example of a rational function that fulfills the description. a. A rational function that has a vertical asymptote at -5 and a hole at 7. b. A rational function that

Question 1104564: Give an example of a rational function that fulfills the description.
a. A rational function that has a vertical asymptote at -5 and a hole at 7.
b. A rational function that has no vertical asymptote and does have a slant asymptote.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
first needs (x+5) in the denominator.
a hole at 7 would require (x-7)/(x-7)
function is (x-7)/(x^2-2x-35)

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denominator has to exist for all x. Can use (x^2+1)
numerator has a higher power x, such as x^3.
(2x^3-3x^2+2x-3)/(x^2+1), where the numerator is the product of (x^2+1)(2x-3)-5, the -5 just to show something more than a line.

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