This may seem like a stupid question, and I do feel like I should know this.
I have been given a simple curve with the following equation and was asked to state the equation of the asymptote of the curve. $$y=\frac{x+1}{x^2+3}$$ I've now discovered that there is an asymptote at $y=0$ but cannot see why this is the case just from looking at the equation.
What about this equation tells us that the x-axis is an asymptote to the curve?
It's because $${\lim}_{x \rightarrow +\infty} \frac{x+1}{x^2+3} = 0$$ and$${\lim}_{x \rightarrow -\infty} \frac{x+1}{x^2+3} = 0.$$
Generally, if limit of a function is $c$ as $x$ tends to infinity, then graph of this function has horizontal asymptote $y=c$.