Hey can someone help me? thanks Select the correct answer.
Function ris a continuous rational function with a horizontal asymptote at y = -8.
Which statement describes the key features of s(t) = (x +2) – 12
A. Function s is continuous and has a horizontal asymptote at y = -1.
В. Function shas a point of discontinuity at I = -2 and a horizontal asymptote at y= -9.
C. Function s has a point of discontinuity at r = -2 and a horizontal asymptote at y = -1.
D. Function sis continuous and has a horizontal asymptote at y = -9.

s(x) is continuous and has a horizontal asymptote at y = -9

We know that we have a function r(x) that has a horizontal asymptote at y = -8

Then, what can we say about the function s(x) = r(x + 2) - 1 ?

Ok, first remember that a horizontal asymptote means that as x, the variable, increases (or decreases), the function eventually tends to a given value, but never actually reaches it.

So as x tends to infinity, we should see an almost horizontal line that tends to y = -8.

So if that happens when x tends to infinity, the same thing will happen when x + 2 tends to infinity, because that "+2" does not add a lot.

Then is easy to conclude that:

r(x + 2) also has a horizontal asymptote at y = -8

And our function is:

s(x) = r(x + 2) - 1

So we are subtracting one, then that horizontal asymptote will be at:

y = -8 - 1 = -9

The function s(x) has a horizontal asymptote at y = -9

And because r(x) is continuous, then:

s(x) = r(x + 2) - 1

is also continuos, as there is nothing added that could change the continuity (we do not have any zero in the denominator or something like that)

Then the correct option is D.

"s(x) is continuous and has a horizontal asymptote at y = -9"

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