A function with function description is
increasing if the function values increase as increases;
decreasing if the function values decrease as increases.
Furthermore, the function has
a maximum when it goes from increasing to decreasing and the graph is continuous;
a minimum when it goes from decreasing to increasing and the graph is continuous.
The maximum and the minimum values are called the extreme values of the function.
The behaviour of a function can be classified more precisely:
increasing (decreasing) constantly when the rate at which the function increases (decreases) is constant
increasingly increasing (decreasing) when the slope of the curve becomes steeper;
decreasingly increasing (decreasing) when the slope of the curve becomes less steep.
To indicate where a function is decreasing/increasing you use intervals.
An interval is a part of the number line. You denote an interval by writing down the boundary values (separated by a comma, the smallest value first) between two parentheses. Two things are important to remember:
the shape of the parentheses determines whether the boundary value is part of the interval or not;
use an arrow for intervals that do not have a boundary at one end.
Here are some examples of intervals and the corresponding part of the number line.