Question

How do the graphs of y = 1/x and y = 5/x+6 compare?

Answer 1

the graph of y = 1/x is a hyperbola it has a vertical asymptote at x = 0 and horizontal asymptote at y = 0



in your 2nd equation you can't have x = -6 in the denominator, because this will give a zero denominator value which is undefined.

so the graph has a vertical asymptote at x = -6

the hotizontal asymptote is still y = 0

so its similar to y = 1/x just moved left...

you can always use a table of values to find some points...

e.g.