How do you identify all horizontal and slant asymptote for $f (x) = 2 + \frac{5}{x^{2} + 2}$ $f(x)=2+5/(x^2+2)$ ?

Question

1070 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-20T01:37:46

y = 2.

$y > 2$ $y> 2$

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, $y \in (2, 4.5]$ $y in (2,4.5]$ .

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

How do you identify all horizontal and slant asymptote for f(x)=2+5/(x^2+2)f(x)=2+5x2+2f(x)=2+5/(x^2+2)?