Increasing and Decreasing Functions
DEFINITIONS
increasing/decreasing functions
A function $\,f\,$ increases on an interval $\,I\,$
if and only if
whenever $\,a \lt b\,$ in $\,I\,,$
$\,f(a) \lt f(b)\,.$
A function $\,f\,$ decreases on an interval $\,I\,$
if and only if
whenever $\,a \lt b\,$ in $\,I\,,$
$\,f(a) \gt f(b)\,.$
an increasing function
a decreasing function
Roughly:
- Increasing means going strictly uphill, as you move from left to right on a graph.
- Decreasing means going strictly downhill, as you move from left to right on a graph.