What are the asymptotes of y=2/x+3 and how do you graph the function?

Feb 9, 2018

$y = 3$
$x = 0$

Explanation:

I tend to think of this function as a transformation of the function $f \left(x\right) = \frac{1}{x}$, which has a horizontal asymptote at $y = 0$ and a vertical asymptote at $x = 0$.

The general form of this equation is $f \left(x\right) = \frac{a}{x - h} + k$.

In this transformation, $h = 0$ and $k = 3$, so the vertical asymptote is not shifted left or right, and the horizontal asymptote is shifted up three units to $y = 3$.

graph{2/x+3 [-9.88, 10.12, -2.8, 7.2]}