Final answer:
A discontinuity occurs when a function is not defined or is not continuous at a certain point. A zero of a function is the value of the input that makes the function equal to zero.
Step-by-step explanation:
A discontinuity of a function occurs when there is a point in the domain where the function is not defined or is not continuous. It can be a removable discontinuity, where the function has a hole at that point, or a non-removable discontinuity, where the function has a jump or vertical asymptote at that point.
A zero of a function occurs when the output of the function is zero. In other words, it is the value of the input that makes the function equal to zero. It can be found by setting the function equal to zero and solving for the variable.