Question

How do you find all the asymptotes for function `f(x) = (7x+1)/(2x-9)`?

Answer 1

First we find the vertical asymptote.
That is when the numerator gets near to `0`:
`2x-9~~0->x~~4 1/2`

The horizontal is found when we make `x` larger and larger. The `+1` and `-9` then matter less and less, and the funtion begins to approach `f(x)~~(7x)/(2x)=7/2=3 1/2`
graph{(7x+1)/(2x-9) [-65.8, 65.9, -32.95, 33]}