identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). state the domain of f.

Explanation:

Step1: Identify vertical asymptotes

Vertical asymptotes occur where the function approaches infinity or negative - infinity. From the graph, as (x) approaches (- 4), the function (y = f(x)) approaches positive or negative infinity. So, the vertical asymptote is (x=-4).

Step2: Identify horizontal asymptotes

As (x\to\pm\infty), the function (y = f(x)) approaches (y = - 2). So, the horizontal asymptote is (y=-2). There are no oblique asymptotes since the function approaches a horizontal line as (x\to\pm\infty).

Step3: Determine the domain

The domain of a function is all the possible (x) - values. Since the only value of (x) for which the function is not defined is (x=-4) (due to the vertical asymptote), the domain is all real numbers except (x = - 4), which can be written as ((-\infty,-4)\cup(-4,\infty)).

Answer:

Vertical asymptote: (x = - 4); Horizontal asymptote: (y=-2); Domain: ((-\infty,-4)\cup(-4,\infty))