Question

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

Answer 1

`y=3`
`x=0`

Explanation:

I tend to think of this function as a transformation of the function `f(x)=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(x)=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]}