## Monotonic Functions

Some functions are increasing for all x and others are decreasing for all x.

For an increasing function an increase in x produces an increase in y so that

For a decreasing function an increase in x produces a decrease in y. so that

Other functions have intervals on which the function is increasing and intervals where it is decreasing.

If a function is increasing or decreasing it is said to be monotonic. If it is increasing or decreasing on an interval it is said to be monotonic on that interval.

is monotonically increasing forand monotonically decreasing for