Change > In graphs
12345In graphs

Theory

A function f with rule y = f ( x ) 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

previous | next