Finding a Discontinuity
Posted: Fri Jul 10, 2026 3:32 pm
Finding a Discontinuity in a function, also known as a "hole", involves factoring a function, if possible, and looking for removable factors
This factor is set to 0 and solved for x, and next, to find the y coordinate of the discontinuity, the removable factors are taken out and the x value is plugged into what's left.
\(\dfrac{(x + 1)(x - 1)}{(x + 1)}\)
\(The\,\,x\,\,part\,\,of\,\, the\,\,discontinuity\,\,is:\)
\((x + 1) = 0\)
\(x = -1\)
\(The\,\,y\,\,part\,\,of\,\,the\,\, discontinuity \,\,is:\)
\(y = (x - 1)\)
\(y = ((-1) - 1)\)
\(y = -2\)