Final answer:
A non-removable discontinuity, also known as a hole, is a point on a graph where the function is undefined but can be defined at that point by assigning a value to it. It occurs when a point on the graph is not included because there is a factor that cancels out and causes a hole in the graph instead of a vertical asymptote or horizontal asymptote.
Step-by-step explanation:
A non-removable discontinuity, also known as a removable singularity, is a point on a graph where the function is undefined but can be defined at that point by assigning a value to it. One example of a non-removable discontinuity is a hole in the graph. A hole occurs when a point on the graph is not included because there is a factor that cancels out and causes a hole in the graph instead of a vertical asymptote or horizontal asymptote. In other words, the function has a hole when it can be factored and simplified to cancel out a factor in the denominator.