Asymptote

Property An asymptote is a boundary line that the graph of a function approaches but never touches or crosses. For a function in the form $y = \frac{a}{x b} + c$, the vertical asymptote occurs at $x=b$ and the horizontal asymptote occurs at $y=c$. Explanation Imagine your graph is a super shy puppy and the asymptote is an invisible electric fence. The puppy can get really, really close to the fence, sniffing along the edge from either side, but it will never actually touch or cross it. These invisible 'fences' are essential guides that define the shape of your graph and its boundaries. Examples For the function $y = \frac{5}{x 3} + 2$, the vertical asymptote is $x=3$ and the horizontal asymptote is $y=2$. For the function $y = \frac{ 4}{x+6} 1$, the vertical asymptote is $x= 6$ and the horizontal asymptote is $y= 1$. For the function $y = \frac{1}{x}$, the vertical asymptote is $x=0$ and the horizontal asymptote is $y=0$.