# How do you find the vertical, horizontal or slant asymptotes for #f(x) = (1/x) + 3#?

##### 1 Answer

Jan 2, 2017

Horizontal:

Vertical :

#### Explanation:

graph{x(y-3)(x(y-3)-1)=0x^2 [-20, 20, -10, 10]}

Tn the quadratic form,

As

Likewise,

as

So,

the vertical asy,ptote is x = 0 and

the horizontal asymptote is y = 3.#.

Note

The equation

hyperbola having the guiding asymptotes

The hyperbola is rectangular, if

Here, from (1), it is immediate that

x(y-3)=0 gives the pair of perpendicular asymptotes.

See the Socratic graph.

.