A vertical asymptote is a vertical line that a graph approaches but never actually touches or crosses. It's usually seen where a function "blows up," meaning the function’s values become infinitely large or small as you get closer to certain values of x.

Vertical asymptotes have the equation x=a for some a∈R.

Vertical asymptotes occur for functions of the form

when h(x)=0 and g(x)=0, as division by zero is undefined, and division by a number close to zero gives a large number.

Example

Find the equation of the vertical asymptote of y=x3−x+11​ using a calculator. Give your answer to 2 significant figures.

Using a calculator, we find x3−x+1=0 when x≈−1.32.