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.

Question 1104806: 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.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the rational function is (x-7) * (x^2 + 3) /((x - 7) * (x+5)).

the range of the function is undefined at x = 7 and x = -5.

there is an asymptote at x = -5.

there is a hole at x = 7.

there is a hole at x = 7 because the factors of (x-7) in the numerator and (x-7) in the denominator cancel out and disappear after simplification.

there is an asymptote at x = -5 because the (x-5) in the denominator is still there after simplification.

here is the graph.

$$$

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