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?
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)