# How do you find all the asymptotes for function #y=(2x^2 + 5x- 3)/(3x+1)#?

##### 2 Answers

See the explanation.

#### Explanation:

The line

There is no horizontal asymptote, because as

If "all the asymptotes" includes oblique asymptotes, then do the division to get:

So

**Vertical Asymptote:**

**Slant Asymptote: **

#### Explanation:

**Vertical Asymptote**

To get the vertical asymptote, find the value of

The vertical asymptote is

**Horizontal/Slant Asymptote**

Since the degree of the numerator is greater than the degree of the denominator by one, we will get a slant asymptote. To solve this, divide

(Sorry for my handwriting)

Never mind the remainder. The only thing you have to take note of is the polynomial on top.

The slant asymptote is