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.

Step 1: Find lim ₓ→∞ f(x). i.e., apply the limit for the function as the x→∞.
Step 2: Find lim of ₓ→ -∞ f(x).
Step 3: If either of the above limits are real numbers then represent the horizontal asymptote as y = k where k represents the value of the limit.

What does it mean for a function to be continuous?

A real function f is continuous if it is continuous at every point in the domain of f. We can explain this in detail with mathematical terms as Suppose f is a function defined on a closed interval, then for f to be continuous, it needs to be continuous at every point, including the endpoints a and b. Continuity of f(x) at a means

What is the point of discontinuity of a function?

If f is not continuous at c, then we can say that f is discontinuous at c, and c is called a point of discontinuity of the given function f. The other way of defining the continuous function is given below. A real function f is continuous if it is continuous at every point in the domain of f.

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