calculus - directional derivatives and continuity

FOR A TWO VARIABLE FUNCTION $f(x,y)$,

I understood that the directional derivative at a point $(x_0,y_0)$ along direction of $\vec u$ is the derivative of the 2D graph that we obtain on the plane kept perpendicular to $xy$ plane passing through the point $(x_0,y_0)$ and parallel to u.

But for 2D graphs to be differentiable , it must be continuos.which means if directional derivative exist along some direction, then the function should be continuous in that direction.

Then how this statement is true:"a fun may be discontinuous even if all directional derivative exists"??

IT WOULD BE REALLY HELPFUL IF U CAN EXPLAIN WITH MY APPROACH