# Can an asymptote be an inflection point?

##### 2 Answers

Since an inflection point is a point on an equation, I assume you mean

"Can an asymptote intersect the line of an equation at an inflection point?"

Under current/modern usage of the concept of asymptote, the answer is a simple "yes";

for example,

Older, more traditional definitions of "asymptote" included a restriction that the equation could not cross the asymptote infinitely; so the given example would not be valid.

However it is possible to imagine a situation like that pictured below

which would still be valid under traditional definitions:

The function:

The graph of this function is concave down on

I have known students to **incorrectly** say that

Note that: an inflection point is **a point on the graph** where the concavity changes. There is no point of the graph of

As Alan P. said in his answer, a graph can have a point of inflection that lies on its asymptote.