what is the horizontal asymptote? y=-2 x=-2 x = 2 y = 2

Explanation:

Step1: Recall asymptote definition

A horizontal asymptote is a horizontal line that the graph of a function approaches as (x\to\pm\infty). It is of the form (y = k), where (k) is a constant. Vertical asymptotes are of the form (x = a).

Step2: Eliminate vertical - asymptote options

Options (x=-2) and (x = 2) are vertical asymptotes since they are in the form (x=a), so we can rule them out.

Step3: Determine the horizontal asymptote

We are left with (y=-2) and (y = 2). Without the function, we just need to know the form of a horizontal asymptote. Since it is (y = k), and we need to pick from the remaining options.

Answer:

If we assume a general case of choosing a horizontal - asymptote from the given options, we have two possible horizontal asymptotes (y=-2) and (y = 2). But if we just need to choose one based on the multiple - choice nature, we note that horizontal asymptotes are (y) - values. So the possible answers for horizontal asymptotes from the given choices are (y=-2) and (y = 2). If we had to pick one randomly (since no function is given), we could say either one is a potential horizontal asymptote. But if we follow the multiple - choice format strictly, the correct options for horizontal asymptotes are: A. (y=-2) D. (y = 2)