Show that y=1 is a horizontal asymptote of the function f(x) = 1/x + 1

To determine if y = 1 is a horizontal asymptote of the function f(x) = 1/x + 1, we need to evaluate the limit of the function as x approaches positive or negative infinity. As x approaches positive infinity: lim(x->∞) (1/x + 1) To find the limit, we simplify the expression: lim(x->∞) (1/x) + lim(x->∞) 1 As x approaches infinity, 1/x approaches 0, and the limit of 1 is 1: 0 + 1 = 1 Therefore, as x approaches positive infinity, f(x) approaches 1. As x approaches negative infinity: lim(x->-∞) (1/x + 1) Again, we simplify the expression: lim(x->-∞) (1/x) + lim(x->-∞) 1 As x approaches negative infinity, 1/x approaches 0, and the limit of 1 is 1: 0 + 1 = 1 Therefore, as x approaches negative infinity, f(x) approaches 1. Since the limits as x approaches positive or negative infinity are both equal to 1, we can conclude that y = 1 is a horizontal asymptote of the function f(x) = 1/x + 1.