Function r is a continuous rational function with a horizontal asymptote at x = -8. Which statement describes the key features of s(x) = r(x + 2) − 1?

A. Function s has a point of discontinuity at x = -2 and a horizontal asymptote at x = -1.
B. Function s has a point of discontinuity at x = -2 and a horizontal asymptote at x = -9.
C. Function s is continuous and has a horizontal asymptote at x = -1.
D. Function s is continuous and has a horizontal asymptote at x = -9.

The correct option for the function taken as r/(x + 2) - 1, is;

A. Function s has a point of discontinuity at x = -2 and a horizontal asymptote at x = -1

Step-by-step explanation:

The asymptote of the given function = Horizontal asymptote at x = -8

Therefore, the degree of the numerator and the denominator are equal and the asymptote = The ratio of the coefficient of largest exponent of the numerator and the denominator

Therefore, when we have the function r(x + 2) - 1, we have that since the largest exponent of the numerator in now larger than the largest exponent of the denominator, we have;

Thee function r(x + 2) - 1, has no asymptote

However, whereby the function is correctly written as r/(x + 2) - 1, we have that given that the function r/(x + 2), has an asymptote of 0 because the largest power of the denominator is bigger than the largest power of the denominator. the function, r/(x + 2) - 1, will have an asymptote at x = -1 and a discontinuity at x + 2 = 0 or x = -2.

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step-by-step explanation:

the true statements are:

r = set of real numbers

n = set of natural numbers, 1,2,

w = n u{0} = {0,1,}