Question

How do you graph `f(x)= (2x^2+7x-15) / (x+5)` and identify all the asymptotes and domain?

Answer 1

`D=ℝ`
`"No asymptotes."`

Explanation:

First thing you should always do is simplify, as you can see, the numerator can be simplified by `(x+5)(2x-3)`:

`f(x)=((x+5)(2x-3))/(x+5)=(cancel((x+5))(2x-3))/cancel((x+5))=2x-3`

`f(x)=2x-3`

and this is really simple, it's a line with a slope of `2` and the intercept point in `(0,-3)`.

graph{2x-3 [-8.91, 8.875, -4.79, 4.1]}