Decreasing Function
If [latex]\left[a,b\right][/latex] is an interval in the domain of a function [latex]f[/latex], we say that the function [latex]f[/latex] is decreasing in the interval [latex]\left[a,b\right][/latex] if and only if for all elements [latex]x_{1}[/latex] and [latex]x_{2}[/latex] of [latex]\left[a,b\right][/latex], if [latex]x_{1}<x_{2}[/latex], then [latex]f\left( x_{1}\right) ≥ f\left(x_{2}\right)[/latex].
Example
Consider the function defined by [latex]f\left(x\right) = -3x+2[/latex].- If [latex]x_{1}=0[/latex], then [latex]f\left(0\right) = 2[/latex].
- If [latex]x_{2}=2[/latex], then [latex]f\left(2\right) = -4[/latex].
