I suppose you need to recognize that the graph only has a horizontal asymptote to the left, none to the right. That asymptote being the negative x-axis , i.e. y = 0 as x → -∞ .
The graph is a reflection through the y-axis of
For the cases you mention, it's handy to be able to visualize the resulting graphs for adding/subtracting functions & multiplying/dividing functions.