look at the graph:\nwhat is the equation of the horizontal asymptote?
look at the graph:\nwhat is the equation of the horizontal asymptote?
Answer
Explanation:
Step1: Recall horizontal asymptote definition
A horizontal asymptote is a horizontal line ((y = k)) that the graph of a function approaches as (x) approaches (+\infty) or (-\infty).
Step2: Analyze the graph's behavior
Looking at the graph, as (x) moves towards (+\infty) (to the right) and as (x) moves towards (-\infty) (to the left, except near the vertical asymptote), the graph approaches the line (y = 0)? Wait, no, wait. Wait, looking at the lower part: the right - hand part of the graph (as (x) increases) is approaching (y = 0)? Wait, no, the graph on the right (for positive (x)) is a horizontal line? Wait, no, the graph: the lower curve, as (x) goes to the right, it's approaching (y = 0)? Wait, no, the horizontal line that the graph approaches. Wait, the graph has a horizontal asymptote. Let's check the (y) - value that the graph approaches as (x) goes to (\pm\infty) (except near the vertical asymptote at (x=- 5)). The right - hand side of the graph (for (x>0)) is a horizontal line? Wait, no, the graph: the lower part, as (x) increases, the (y) - value approaches (y = 0)? Wait, no, looking at the graph, the horizontal asymptote is (y = 0)? Wait, no, wait the graph: the part for (x\geq0) is a horizontal line along (y = 0)? Wait, the graph's right - most part is along (y = 0), and as (x) approaches (+\infty), (y) approaches (0), and as (x) approaches (-\infty) (the left - hand curve, not near (x = - 5)), it also approaches (y = 0)? Wait, no, the left - hand curve (for (x<-5), the lower one) as (x) approaches (-\infty), (y) approaches (0). So the horizontal asymptote is (y = 0)? Wait, no, wait the graph: let's re - examine. The horizontal asymptote is the horizontal line that the function approaches. From the graph, the function approaches (y = 0) as (x\to\pm\infty). Wait, but maybe I made a mistake. Wait, the graph: the right - hand side (for (x) positive) is a horizontal line at (y = 0), and the left - hand side (the lower curve, for (x<-5)) as (x) goes to (-\infty), it approaches (y = 0). So the equation of the horizontal asymptote is (y = 0).
Answer:
(y = 0)