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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)

Respuesta :

Answer:

[tex] \frac{x + 2}{ {x}^{2} - x - 20 } [/tex]

Step-by-step explanation:

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

[tex](x + 4)(x - 5)[/tex]

Apply foil method to find our denominator.

We get

[tex] {x}^{2} - x - 20[/tex]

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

[tex](x + 2)[/tex]

So our rational denomiater is

[tex] \frac{x + 2}{ {x}^{2} - x - 20 } [/tex]

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