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 \(x_1,x_2∈A, x_1<x_2\)