Search for a tool
Decreasing Function

Tool to calculate if a function is decreasing / monotonic or on which interval is decreasing or strictly decreasing.

Results

Decreasing Function -

Tag(s) : Functions

Share
dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Thanks to your feedback and relevant comments, dCode has developed the best 'Decreasing Function' tool, so feel free to write! Thank you!

# Decreasing Function

## Decreasing Function Calculator

 Monotony Strictly decreasing Weakly decreasing

### What is a decreasing function?

A function $f$ is strictly decreasing if for any $$x_1 < x_2, f(x_1) < f(x_2)$$ (signs are inverted)

In other words, $f$ has a decreasing direction of variation, when $x$ decreases, $f(x)$ also decreases (not necessarily by the same quantity).

A function is said to be decreasing (not strictly, in the broad sense) if for all $$x_1 < x_2, f(x_1) \leq f(x_2)$$

Example: The function $f(x) = x + 1$ is decreasing over its whole domain of definition $\mathbb {R}$

The decrease of a function can also be defined over an interval.

Example: The function $f(x) = x^2$ is strictly decreasing over $\mathbb{R}^+$ also noted $x < 0$ or also $] -\infty ; 0 [$

### How to determine if a function is decreasing?

Several methods allow to to find the direction of variation for knowing if a function is decreasing:

- From its derivative: When the derivative of the function is less than $0$ then the function is decreasing.

Example: The derivative of the function $f(x) = x^2+1$ is $f'(x) = 2x$, the calculation of $f'(x) > 0$ gives $x > 0$ so the function $f$ is decreasing when $x > 0$

- From its equation : Some functions are notoriously decreasing, ie. the inverse function, the opposite of increasing functions, etc.

Example: $\frac{1}{x}$ is decreasing over $\mathbb{R}^*$

- From the curve of the function: a decreasing function has its curve which is directed downwards.

### How to determine if a linear/affine function is decreasing?

A linear function of the form $f(x) = ax + b$ is decreasing over $\mathbb{R}$ when the coefficient $a$ is positive ($a < 0$). If $a$ is positive then the function is increasing.

## Source code

dCode retains ownership of the online 'Decreasing Function' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any 'Decreasing Function' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Decreasing Function' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Decreasing Function' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

## Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!