key term - Intermediate Value Theorem

Definition

The Intermediate Value Theorem states that if a continuous function takes on two values, say "a" and "b", at two points in its domain, then it must also take on every value between "a" and "b" at some point within that domain.

Related terms

Root: In mathematics, a root refers to finding the value(s) of an equation or expression that make it equal to zero. It represents the x-values where a function intersects with the x-axis.

Bolzano's Theorem: Bolzano's theorem is another name for the Intermediate Value Theorem. It was named after Bernard Bolzano, who first stated this important result.

Monotonicity: Monotonicity describes whether a function is increasing or decreasing over its entire domain. A monotonic function either always increases or always decreases as you move from left to right on its graph.