Question

Find the horizontal asymptote of the graph of the rational function. y = 3 ——— x + 2 Identify the horizontal asymptote for the graph of the function.

Answer 1

A horizontal asymptote is a horizontal line that is not part of a graph of a function but guides it for x-values. “far” to the right and/or “far” to the left. The graph may cross it but eventually, for large enough or small.

To calculate the horizontal asymptote, we calculate the end behavior of the function on both ends.

$\begin{gathered} \lim_{x\to\infty}\frac{3}{x+2}=0 \\ \lim_{x\to-\infty}\frac{3}{x+2}=0 \end{gathered}$

The horizontal asymptote is

$y=0$