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# 1.7: Increasing and Decreasing Functions

Difficulty Level: At Grade Created by: CK-12
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### Vocabulary Language: English

Continuous

Continuous

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.
decreasing

decreasing

A function is decreasing over an interval if its $y$ values are getting smaller over the interval. The graph will go down from left to right over the interval.
decreasing function

decreasing function

A decreasing function is one with a graph that goes down from left to right.
Function

Function

A function is a relation where there is only one output for every input. In other words, for every value of $x$, there is only one value for $y$.
Global Maximum

Global Maximum

The global maximum of a function is the largest value of the entire function. Symbolically, it is the highest point on the entire graph.
Global Minimum

Global Minimum

The global minimum of a function is the smallest value of the entire function. Symbolically, it is the lowest point on the entire graph.
increasing

increasing

A function is increasing over an interval if its $y$ values are getting larger over the interval. The graph will go up from left to right over the interval.
increasing function

increasing function

An increasing function is one with a graph that goes up from left to right.
interval

interval

An interval is a specific and limited part of a function.
Interval Notation

Interval Notation

Interval notation is the notation $[a, b)$, where a function is defined between $a$ and $b$. 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.
monotonic

monotonic

A function is monotonic if it does not switch between increasing and decreasing at any point.
relative extrema

relative extrema

The relative extrema of a function are the points of the function with $y$ values that are the highest or lowest of a local neighborhood of the function.
strictly

strictly

Strictly is an adjective that alters increasing and decreasing to exclude any flatness or periods where $y$ values are staying constant.

Nov 01, 2012

Jun 08, 2015