Question

use the graph to answer the question. name the asymptote for the graphed function. (1 point) x = 2 x = 4 y = 2 y = 4

Explanation:

Step1: Recall the definition of a horizontal asymptote

A horizontal asymptote is a horizontal line \(y = k\) that the graph of a function approaches as \(x\to\pm\infty\). A vertical asymptote is a vertical line \(x = a\) that the graph approaches as \(y\to\pm\infty\).

Step2: Analyze the graph

Looking at the given graph, as \(x\to-\infty\), the \(y -\) values of the function approach \(y = 2\). There is no vertical line \(x=a\) that the graph approaches (since the function is defined for all real \(x\) values in the context of the graph shown, and as \(x\) increases, the function grows without bound and as \(x\) decreases, it approaches a horizontal line).

Answer:

\(y = 2\)