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

Nov 25, 2017

D=ℝ
$\text{No asymptotes.}$

#### Explanation:

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

$f \left(x\right) = \frac{\left(x + 5\right) \left(2 x - 3\right)}{x + 5} = \frac{\cancel{\left(x + 5\right)} \left(2 x - 3\right)}{\cancel{\left(x + 5\right)}} = 2 x - 3$

$f \left(x\right) = 2 x - 3$

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

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