# How do you find discontinuity points?

Graphically, a discontinuity can be located at places where the function appears to "jump", oscillates wildly, goes to $\pm \infty$, or has a "hole". Analytically, one looks for $x$-values where the right and left-hand limits of the function have odd behaviors; fluctuating wildly, trending towards $\pm \infty$, being unequal to one another, or being unequal to the value of the function at that point.