In this paper, we study the global attractivity, the invariant intervals, the periodic and oscillatory character of the difference equation where a, b, A, B are positive real numbers, k≥1 is a positive integer, and the initial conditions x _−k ,…,x ₋₁,x ₀ are nonnegative real numbers such that x _−k or x ₀ or both are positive real numbers. We show that the positive equilibrium of the difference equation is a global attractor. As a corollary, our main result confirms a conjecture proposed by Kulenović et al. () [The dynamics of facts and conjectures, Computational Mathematics Applications, 45, 1087–1099].