Why do the graphs of reciprocals of linear functions always have vertical asymptotes, but the graphs of reciprocals of quadratic functions sometimes do not? Justify with an example.

Answer 1

except for horizontal lines, there is a point where y=0
The reciprocal would have you divide by zero, which is undefined.

Some quadratic functions, such as y = x^2+1 are never zero, so 1/y is always defined.