y = 3/x:
y = 3/x + 4
This graph has about the same characteristics as the previous graph. Let us now overlay the two graphs to see the difference between them.
As it can be seen, the 2nd graph was "raised" by approximately 4 points. As such, we can see that any extra values added to the original equation has the effect of raising the graph.
Let us try another graph.
y = -1/x
y = -1/x - 4
The graph has the same characteristics, and it can be seen that it is "lowered" by 4. Now, we can also see that subtracting values also affects the graph.
Y = 0/X
y = 1/(x-2)
The graph is shifted slightly to the right, causing the bottom asymptote to intersect the y-axis. Otherwise, the graph has the same characteristics.
Let us over lay a line x = 2 on the graph.
As can be seen, the vertical asymptotes are towards the line x = 2. As y approaches +-∞, x approaches 2, but does not reach 2.