Change > In graphs
12345In graphs

## Theory

A function $f$ with rule $y=f\left(x\right)$ is called

• increasing if the value of the function becomes larger as $x$ increases;

• decreasing if the value of the function becomes smaller as $x$ increases.

A function can have

• a maximum if there is a transition from increasing to decreasing without a break in the line;

• a minimum if there is a transition from decreasing to increasing without a break in the line.

The points at which these transitions occur are called the extrema (singular: extremum) of the function.

You can see different types of increase and decrease in a function:

• a constant increase (decrease) if the function continues to increase (decrease) with the same (constant) rate;

• an accelerated increase (decrease) if the rate of increase (decrease) becomes larger as $x$ increases;

• a decelerated increase (decrease) if the rate of increase (decrease) becomes smaller as $x$ increases