We study the change of dynamics of transcendental meromorphic functions f λ = λ e z z+1 for z ∈ C when λ varies on the negative real axis. It is shown that there is a λ such that the Fatou set of f λ is empty for λ < λ whereas the Fatou set is an invariant parabolic basin corresponding to a real rationally indifferent fixed point x if λ = λ. In fact, the Fatou set is an invariant attracting basin of a real negative fixed point a λ if λ < λ < 0. Also the dynamics of f n λ for n ≥ 2 at the fixed points is investigated for different values of λ. As a generalization of f λ , we observed some dynamical issues for the class of entire maps F λ,a,m (z) = λ(z + a) m exp(z) where λ, a ∈ C and m ∈ N