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

1 Answer
Nov 25, 2017

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]}