In this article, we will study the concept of increasing and decreasing functions, their properties, graphical representation, and theorems to test for increasing and decreasing functions along with …

Strictly Increasing (and Strictly Decreasing) functions have a special property called "injective" or "one-to-one" which simply means we never get the same "y" value twice. Why is this useful? Because …

Nov 27, 2025 · A function is considered increasing if for any two values x1 and x2 such that x1 < x2 , the function value at x1 is less than the function value at x2 (i.e., f ( x1) < f ( x2)). On the other hand, a …

Jun 20, 2025 · Learn about increasing and decreasing functions for your A level maths exam. This revision note covers what they are and how to identify them.

6 days ago · The first derivative of a function reveals where the original function is increasing, decreasing, or remains monotonic over specific intervals.

Dec 1, 2025 · In this lesson we will consider the function values in between extrema (extremes: minimums or maximums), focusing on where function values are increasing or decreasing. A function …

Function f (x) = x 2 f (x) = x2 is increasing on interval [0, ∞) [0,∞) and decreasing on interval (∞, 0) (−∞,0). The only difference between increasing and non-decreasing, decreasing and non-increasing …

For differentiable functions, if the derivative of a function is positive on an interval, then it is known to be increasing while the opposite is true if the function's derivative is negative.

May 16, 2025 · Explore how to identify increasing and decreasing functions in Algebra I with clear definitions, examples, and graph-based strategies.

Similarly, a function is decreasing on an interval if the function values decrease as the input values increase over that interval. The figure below shows examples of increasing and decreasing intervals …