# How do you identify all horizontal and slant asymptote for f(x)=2+5/(x^2+2)?

Dec 20, 2016

y = 2.

#### Explanation:

$y > 2$

As # x to +-oo, y to 2. So,

y = 2 is the horizontal asymptote.

y-intercept (x = 0 ) is the maximum y, 4.5

Thus, $y \in \left(2 , 4.5\right]$.

graph{(x^2+2)(y-2)-5=0 [-20, 20, -10, 10]}