Continuity for a point exists when the left and right sided limits match the function evaluated at that point. For a function to be continuous, the function must be continuous at every single point in an unbroken domain.
A function is decreasing over an interval if its values are getting smaller over the interval. The graph will go down from left to right over the interval.
A decreasing function is one with a graph that goes down from left to right.
A function is a relation where there is only one output for every input. In other words, for every value of , there is only one value for .
The global maximum of a function is the largest value of the entire function. Symbolically, it is the highest point on the entire graph.
The global minimum of a function is the smallest value of the entire function. Symbolically, it is the lowest point on the entire graph.
A function is increasing over an interval if its values are getting larger over the interval. The graph will go up from left to right over the interval.
An increasing function is one with a graph that goes up from left to right.
An interval is a specific and limited part of a function.
Interval notation is the notation , where a function is defined between and . Use ( or ) to indicate that the end value is not included and [ or ] to indicate that the end value is included. Never use [ or ] with infinity or negative infinity.
A function is monotonic if it does not switch between increasing and decreasing at any point.
The relative extrema of a function are the points of the function with values that are the highest or lowest of a local neighborhood of the function.
Strictly is an adjective that alters increasing and decreasing to exclude any flatness or periods where values are staying constant.
Identification of increasing and decreasing intervals of discrete and continuous functions.