# How do you find the Vertical, Horizontal, and Oblique Asymptote given #f(x)= (x+5)/(x+3)#?

##### 1 Answer

Jan 1, 2017

Horizontal:

Vertical :

See Socratic graph, with asymptotes.

#### Explanation:

By actual division,

y = Q gives parabolic, ( slant-straight) oblique or horizontal

asymptote according as Q is quadratic, linear or constant,

respectively.

x = zero(s) of S give vertical asymptote(s).

Here,

they are

In the graph, the asymptote

unable to get it out. However, y = 1 is marked.

The graph is the a rectangular hyperbola (y-1)(x+3)=2, with center at

the meet of the asymptotes,

graph{(y-1)(x+3)(y-(x+5)/(x+3))=0 [-11.71, 11.71, -5.85, 5.86]}