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

1 Answer
Feb 9, 2018

y=3y=3
x=0x=0

Explanation:

I tend to think of this function as a transformation of the function f(x)=1/xf(x)=1x, which has a horizontal asymptote at y=0y=0 and a vertical asymptote at x=0x=0.

The general form of this equation is f(x)=a/(x-h)+kf(x)=axh+k.

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

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