Question 1131911
{{{lim(x->infinity)}}}{{{ (4 x^2 - 3)/(x^2 + 1) = 4}}}

A horizontal asymptote is

{{{(4 x^2 - 3)/(x^2 + 1)}}}->{{{4}}} as {{{x}}}-> ±{{{infinity}}}

A horizontal asymptote is in this case a horizontal line  {{{y=4}}} that indicates where a function flattens out as {{{x}}} gets very large or very small. A function may touch or pass through a horizontal asymptote. 



<a href="http://tinypic.com?ref=51zvy1" target="_blank"><img src="http://i64.tinypic.com/51zvy1.gif" border="0" alt="Image and video hosting by TinyPic"></a>


as you can see on the graph, a function didn't touch or pass through a horizontal asymptote