Where is the horizontal asymptote here?

Question

My textbook tells me about 3 cases of how to define whether or not the function in hand has a horizontal asymptote:

Here I have this function:

As far as I understand, I am dealing here with case number 3, that is, the case where the degree of the numerator is the same as the degree of the denominator.

According to the logic of case number 3, the horizontal asymptote is the ratio of the leading coefficients. Since in my formula the leading coefficients are both equal to 1, the ratio then is also equal to 1 (because 1/1 = 1).

However, when I graph that form in a graphical calculator, I see a graph, in which there is no possible horizontal asymptote:

What do I get wrong here?

Answer 1

Quote from wikipedia "Horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞. As the name indicates they are parallel to the x-axis. Vertical asymptotes are vertical lines (perpendicular to the x-axis) near which the function grows without bound". Well you can see that as x tends to +∞ or −∞, the function approaches the line y=1.

Answer 2

You're right! There isn't any mistake. As x tends to $+\infty$ the function is closest and closest to 1. Following the same logic, as x tends to $-\infty$ the function is closest and closest to 1.