What is the discontinuity of the function #f(x) = 1/x# ?

1 Answer
Eddie W.
Jul 30, 2014

The discontinuity for #f(x)=1/x# is at #x=0#.

Discontinuities occur at values of x where the graph can't be evaluated. Since division by 0 is mathematically undefined, we can't plot a point for it on the graph of #1/x#, it represents a break in the graph.

This also means that in this case, there is actually a vertical asymptote with the equation #x=0#.

Related questions
See all questions in Classifying Topics of Discontinuity (removable vs. non-removable)
Impact of this question
12692 views around the world
You can reuse this answer
Creative Commons License