Question

look at the graph:
graph of a function with a horizontal asymptote
what is the equation of the horizontal asymptote?

Explanation:

Step1: Recall horizontal asymptote definition

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

Step2: Analyze the graph's behavior

Looking at the graph, as \( x \) approaches positive infinity and negative infinity, the graph approaches the horizontal line \( y = 0 \)? Wait, no, wait. Wait, looking at the graph: the left part (as \( x \to -\infty \)) approaches a horizontal line, and the right part (as \( x \to +\infty \)) also approaches a horizontal line. Wait, no, wait the graph: the upper right curve approaches a horizontal line, and the lower left curve? Wait, no, the graph has a horizontal asymptote. Wait, looking at the y - axis: the horizontal line that the graph approaches. Wait, the graph on the right (x positive large) is approaching \( y = 0 \)? No, wait, no. Wait, the graph: the right - hand curve is approaching a horizontal line, and the left - hand curve is also approaching a horizontal line. Wait, actually, looking at the graph, the horizontal asymptote is \( y = 0 \)? Wait, no, wait the graph: the horizontal line that the function approaches as \( x \to \pm\infty \). Wait, the graph's horizontal asymptote: when \( x \) goes to positive infinity, the \( y \) - value approaches 0? Wait, no, wait the graph: the right - hand curve is approaching \( y = 0 \)? Wait, no, let's check again. Wait, the graph: the horizontal asymptote is the horizontal line that the graph gets closer and closer to as \( x \) becomes very large (positive or negative). Looking at the graph, as \( x \to +\infty \), the \( y \) - value approaches 0? Wait, no, wait the graph: the right - hand curve is approaching \( y = 0 \)? Wait, no, maybe I made a mistake. Wait, the graph: the horizontal asymptote is \( y = 0 \)? Wait, no, let's see: the horizontal line is \( y = 0 \) (the x - axis). Wait, the graph's horizontal asymptote is \( y = 0 \)? Wait, no, wait the graph: the left - hand curve (as \( x \to -\infty \)) approaches \( y = 0 \), and the right - hand curve (as \( x \to +\infty \)) also approaches \( y = 0 \). Wait, but wait, the graph: the horizontal asymptote is \( y = 0 \)? Wait, no, maybe I misread. Wait, the graph: the horizontal line is \( y = 0 \). So the equation of the horizontal asymptote is \( y = 0 \)? Wait, no, wait the graph: let's look again. The graph has a horizontal asymptote at \( y = 0 \) (the x - axis). Because as \( x \) approaches positive infinity, the \( y \) - coordinate approaches 0, and as \( x \) approaches negative infinity, the \( y \) - coordinate also approaches 0.

Wait, no, wait the graph: the right - hand curve is approaching a horizontal line, and the left - hand curve? Wait, maybe I made a mistake. Wait, the correct way: a horizontal asymptote is a line \( y = k \) such that \( \lim_{x\to\infty}f(x)=k \) or \( \lim_{x\to-\infty}f(x)=k \). Looking at the graph, as \( x\to\infty \), \( f(x)\to0 \), and as \( x\to-\infty \), \( f(x)\to0 \). So the horizontal asymptote is \( y = 0 \).

Answer:

\( y = 0 \)