# Thread: How do you graph the rational function y= x-4/(x^2+2)

1. ## How do you graph the rational function y= x-4/(x^2+2)

$y = x-4/(x^2+2)$

for the graph of

$y = \frac{x-4}{x^2+2}$

for horizontal asymptote, divide numerator and denominator with highest power $(x^2)$ and take $x\rightarrow \infty$

horizontal asymptote is x-axis (equation of x-axis is y=0)

there is no vertical asymptote.

$as\;\; x \rightarrow \infty, \;\;y \rightarrow 0$

$as\;\; x \rightarrow -\infty, \;\;y \rightarrow 0$

also, points (0, -2) and (4,0) lie on the graph.