Increasing Function Definition
In simple words, an increasing function is a type of function where with increasing input (or the independent variable), output also increases (or the value of the function). Now, let’s define increasing function formally.
Now, 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 increasing functions include linear functions with positive slope (such as y = mx + b), exponential functions (such as y = ax, where a is a positive constant), and power functions (such as y = xn, where n is a positive integer).
Strictly Increasing Function
For a function to be strictly increasing, the function should be increasing 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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