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

What are the asymptotes of $y=\frac{2}{x}+3$ and how do you graph the function?
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Ashlynn Cox
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]}