Intermediate Value Theorem (+ some continuity and Limits)

If a function f is continuous on the interval [a, b] and f(a) ≠ f(b), then for every value L between f(a) and f(b), there exists at least one c in (a, b) such that f(c) = L.

A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point.

A function is discontinuous if there is a break, jump, or hole in its graph.

A limit is the value that a function approaches as the input approaches a certain point.

The limit is -2.

There is a zero between -1 and 1 due to the Intermediate Value Theorem.

The interval [1, 2] contains a zero.

A function is continuous if it is uninterrupted and has no breaks in its graph.

It guarantees that if a function changes signs over an interval, there is at least one root in that interval.

DNE stands for 'Does Not Exist', indicating that a limit does not approach a finite value.