Increasing and decreasing functions

Summary

• Given: a real-valued function of a real variable, $f: A→B$ where $A⊆R$ , $B⊆R$
• We say that $f$ is
• increasing if $f\left( x_1 \right)≤f(x_2)$ for all $x_1,x_2∈A, x_1<x_2$
• strictly increasing if $f\left( x_1 \right)<f(x_2)$ for all $x_1,x_2∈A, x_1<x_2$
• decreasing if $f\left( x_1 \right)≥f(x_2)$ for all $x_1,x_2∈A, x_1<x_2$
• strictly decreasing if $f\left( x_1 \right)>f(x_2)$ for all $x_1,x_2∈A, x_1<x_2$