Here be a line, if not the image is missing Remember: Let i be a non-empty interval I ⊆ ℝ.
A function φ : I → ℝ is called monotonically increasing (or decreasing), if

φ (x1 ) ≤ φ(x2)

(or φ ( x 1 ) ≥ φ ( x 2 )) holds true for all x 1 ,x 2 ∈ I where x 1 < x 2 . If equality is excluded, the function is called strictly monotonically increasing (or decreasing)