What are vertical asymptotes?

 

Vertical asymptotes are important boundary lines for a function, because, if you can find them, they're a line that the graph cannot cross, which can really help you sketch a more accurate picture of the curve.

Vertical asymptotes are usually found in rational and logarithmic functions, but they can be found in other functions, too. And, not every rational function or logarithmic function has a vertical asymptote.

But if there is a place along the curve where the graph is undefined, like maybe because the denominator of a fraction in the function is equal to 0, or because the argument inside a logarithm is negative, then you'll have a vertical asymptote at that point.

While the curve will get infinitely close to a vertical asymptote on one or both sides of it, it will never ever cross the asymptote.

 

Want to learn more about Applications of Derivatives? I have a step-by-step course for that. 😃

 

Krista King