Which equation describes a rational function with x-intercepts at –4 and 2, a vertical asymptote at x = 1 and x = –1, and a horizontal asymptote at y = –3?

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veneration veneration · Answer 1 · 2020-10-16T00:04:49+02:00

Answer:

Fourth Option

Step-by-step explanation:

Consider the numerator

x + 4 = 0, x = -4

x = -4 becomes the x intercept

x - 2 = 0, x = 2

Like the question says the two intercepts are x = -4 and x = 2

Now consider the denominator, which will help find the vertical asymptote

x^2 - 1. x = +1, x = -1

Like the question says the vertical asymptote is x=1 and x = -1

The horizontal asymptote is right next to the parentheses

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ayoushivt ayoushivt · Answer 2 · 2022-07-27T09:33:26+02:00

The equation that describes a rational function with the given data is in option D.

A function is a law that relates a dependent and an independent variable.

The rational function that has x intercepts at -4 and 2 is option D

f(x) = ( -3 (x+4) (x-2) /(x²-1))

(x+4) (x-2) = 0

x = -4 , 2

The vertical asymptote is determined by the denominator

x² -1 = 0

x = ±1

x = +1 , x = -1

The horizontal asymptote is determined

y = -3

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