Decreasing Function Definition
In simple words, a decreasing function is a type of function where with increasing input (or the independent variable), the output value decreases (or the value of the function). To define decreasing function formally let us consider I to be an interval that presents in the domain of a real-valued function f, then the function f is increasing on I,
if x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1 and x2 ∈ I
Some common examples of decreasing functions include exponential decay functions (such as y = a^(-x), where a is a positive constant), and negative power functions (such as y = x^(-n), where n is a positive integer).
Strictly Decreasing Function
For a function to be strictly decreasing, the function should be decreasing but it can’t be equal for any two unequal values i.e.,
if x1 < x2 ⇒ f(x1) > f(x2) ∀ x1 and x2 ∈ I
Increasing and Decreasing Functions
If you’re studying calculus, then you’re probably familiar with the concepts of increasing and decreasing functions. These terms refer to the behavior of a function as its input values change. Specifically, an increasing function is one that becomes larger as its input values increase, while a decreasing function is one that becomes smaller as its input values increase. Understanding these concepts is crucial for solving a variety of calculus problems, from finding maximum and minimum values to understanding the behavior of graphs.
In this article, we’ll delve deeper into increasing and decreasing functions, exploring how to identify them, and how to use them to solve problems in calculus.
Table of Content
- Increasing Function Definition
- Decreasing Function Definition
- Constant Function Definition
- Rules to Check Increasing and Decreasing Functions
- Graph of Increasing, Decreasing, and Constant Function
- Properties of Increasing & Decreasing Functions
- How to Find Increasing and Decreasing Intervals
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