How do you find asymptotes with limits at infinity?

A function f(x) will have the horizontal asymptote y=L if either limx→∞f(x)=L or limx→−∞f(x)=L. Therefore, to find horizontal asymptotes, we simply evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity.

Is infinity an asymptote?

If a function has a limit at infinity, it will appear to straighten out into a line as we move farther and farther away from the origin along the x-axis. We can figure out the equation for this line by taking the limit of our equation as x approaches infinity. This line is called an asymptote.

What does it mean if the horizontal asymptote is infinity?

Definition: Horizontal Asymptote. If limx→∞f(x)=L or limx→−∞f(x)=L, we say the line y=L is a horizontal asymptote of f. A function cannot cross a vertical asymptote because the graph must approach infinity (or −∞) from at least one direction as x approaches the vertical asymptote.

Are there limits at infinity and horizontal asymptotes?

Limits at Infinity and Horizontal Asymptotes Recall that lim x → af(x) = L means f(x) becomes arbitrarily close to L as long as x is sufficiently close to a. We can extend this idea to limits at infinity. For example, consider the function f(x) = 2 + 1 x.

How to find out if you have an asymptote?

In order to figure out if we have asymptotes, we will need to evaluate our function using limits. To figure out any potential horizontal asymptotes, we will use limits approaching infinity from the positive and negative direction.

How are limits at infinity and Unbounded Limits represented?

Closes this module. Unbounded limits are represented graphically by vertical asymptotes and limits at infinity are represented graphically by horizontal asymptotes. This is the currently selected item. Posted 3 years ago.

Can a function cross a horizontal asymptote of F?

The line y = M is a horizontal asymptote of f. If lim x → ∞ f(x) = L or lim x → − ∞ f(x) = L, we say the line y = L is a horizontal asymptote of f. A function cannot cross a vertical asymptote because the graph must approach infinity (or − ∞) from at least one direction as x approaches the vertical asymptote.