We acquaint a parametric amplification of a certain family of Bernstein-type rational functions on the interval \([0,\infty )\) . Firstly, we give the construction of these operators and the values at test functions which will be used in evaluating the central moments of them. Then, we explore the characteristics of the weighted approximation theory related to these operators. Next, shape maintaining characteristics of these operators are examined. Finally, the convergence characteristics of these operators to some functions are showed by graphics.