# How do you find the vertical, horizontal or slant asymptotes for #f(x) = (2x^2 + x + 2) /( x + 1)#?

##### 2 Answers

Vertical asymptote at

No horizontal asymptote

Slant asymptote:

#### Explanation:

Given:

giving us the vertical asymptote of

and

so there is no horizontal asymptote.

Since the degree of the numerator is greater than the degree of the denominator,

we can divide the denominator into the numerator to get a slant asysmptote:

So the slant asymptote is

Slant Asymptote:

Vertical Asymptote:

Horizontal Asymptote: None

#### Explanation:

The given function is

To find the slant asymptote, divide numerator by the denominator of the given rational function.

The result of the division is

The whole number part of the quotient which is

which is the

To solve for the Vertical Asymptote, use the divisor and equate to zero

and the Vertical Asymptote is

There is

Kindly see the graph of the function

God bless....I hope the explanation is useful.