Question

question #9 determine the equation of the horizontal asymptote of the rational function. y = 2 y = - 3 x = - 3 x = 2

Explanation:

Step1: Recall horizontal asymptote concept

A horizontal asymptote is a horizontal line that the graph of a function approaches as \(x\to\pm\infty\). For a rational - function, we can also identify it from the graph. In a graph, the horizontal line that the function values get closer and closer to as \(x\) moves to the left or right is the horizontal asymptote.

Step2: Analyze the given graph

Looking at the graph, as \(x\to-\infty\) and \(x\to+\infty\), the \(y\) - values of the rational function approach \(y = 2\). The equation of a horizontal line is of the form \(y = k\), where \(k\) is a constant. The vertical lines \(x=-3\) and \(x = 2\) are vertical asymptotes, not horizontal asymptotes.

Answer:

A. \(y = 2\)