Question

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)

Answer 1

`\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 }`