Question

Find the horizontal asymptotes of

Answer 1

You can enter this: y = (1 - abs(x))/x horizontal asymptote
over at the WolfRam site to view the asymptotes and graph.

http://www.wolframalpha.com/ @master50777

Answer 2

please eliminating the abs symbol, we can write:
\[f(x)=\frac{ 1-x }{ x },x>0\]
and
\[f(x)=\frac{ 1+x }{ x },x<0\]
asymptotes, there are points, whose x-coordinates makes equals to zero the denominator, so at x=0, in our case. In other words, there is an asymptote, whose equation is x=0

Answer 3

more precisely x=0 is a vertical asimptote. In order to find horizontal asymptotes, you have to find the subsequent limits:
\[\lim _{x \rightarrow +\infty} \frac{ 1-x }{ x }=-1,\]
and:
\[\lim _{x \rightarrow-\infty} \frac{ 1+x }{ x }=1\]
So you have two horizontal asymptotes, namely:
y=-1 going to +infinity, at the right side,
and:
y=1,going to left side or to -infinity.