What Are Increasing and Decreasing Functions?
One of the most important questions we can ask about a function is: where is it going up, and where is it going down? This is the study of increasing and decreasing functions — a concept that sits at the heart of curve sketching, optimisation, and real-world modelling.
A function is increasing on an interval if, for any two points and in that interval with , we have . In other words, as moves to the right, the function values go up.
A function is decreasing on an interval if, for any two points and in that interval with , we have . As moves to the right, the function values go down.
These are strict definitions — the function value must be strictly greater or strictly less (not equal) as you move right along the interval.
In some contexts you may encounter non-strictly increasing or decreasing functions, where or respectively. For IB purposes, the strict versions above are standard unless stated otherwise.
