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

# 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. \(y = 2\)