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Find a rational function that satisfies the given conditions. Answers may vary, but try to give the simplest answer possible:

Vertical asymptotes x = -4, x = 5;

x-intercept (-2, 0)

User Sellibitze
by
8.2k points

1 Answer

3 votes

Answer:


\frac{x + 2}{ {x}^(2) - x - 20 }

Explanation:

Since the roots are -4 and 5, we can write that as


(x + 4)(x - 5)

Apply foil method to find our denominator.

We get


{x}^(2) - x - 20

So that our denominator.

Since our denomiater gives us interger asymptote, our degree in our numerator must be 1 so the answer has to be a single interger or a single term.

Since our x intercepts is -2, we use


(x + 2)

So our rational denomiater is


\frac{x + 2}{ {x}^(2) - x - 20 }

User Anjan Talatam
by
8.4k points

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