Final answer:
In mathematics, a function is considered discontinuous if it has a break or jump in its graph. Symbolically, this can be represented using mathematical notation when there is a difference in the limits or when the function is undefined or has a vertical asymptote at a certain point.
Step-by-step explanation:
In mathematics, a function is considered discontinuous if it has a break or jump in its graph. This usually occurs when there is a point in the domain of the function where the function is not defined or where the limit of the function does not exist. Symbolically, we can represent this using mathematical notation. For example, if we have a function f(x) and at a certain point c the limit of f(x) as x approaches c from the left is not equal to the limit of f(x) as x approaches c from the right, we can symbolically represent this as f(c-) ≠ f(c+).
Another symbolic representation of a discontinuity is when the function is undefined or has a vertical asymptote at a certain point in its domain. For instance, if we have a function g(x) and at a certain point d the value of g(x) goes to infinity (or negative infinity), we can symbolically represent this as g(d) = ∞ (or g(d) = -∞).
These symbolic representations help us express the nature of the discontinuity in a concise and precise way.