Explain why the graph of g(x) = 1/x has a horizontal asymptote. What is the equation of this asymptote? Will all reciprocal functions have the same horizontal asymptote?

Answer 1

the larger the divisor, the smaller the quotient. So, as x gets incredibly large, 1/x gets incredibly small.

So, as x gets infinitely large, 1/x gets infinitely small, or zero.

So, yes, all reciprocal functions have y=0 as their horizontal asymptote. (depending on just what you mean by a reciprocal function)