# How do you graph #y=(3x^3+1)/(4x^2-32)# using asymptotes, intercepts, end behavior?

##### 2 Answers

The vertical asymptotes are

The slant asymptote is

No horozontal asymptote.

#### Explanation:

Let's factorise the denominator

The domain of

As we cannot divide by

So

The vertical asymptotes are

As the degree of the numerator is

Let's do a long division

So,

The slant asymptote is

To calculate the limits, we use the terms of highest degree.

There are no horizontal asymptote

When

When

graph{(y-(3x^3+1)/(4x^2-32))(y-x3/4)=0 [-28.86, 28.9, -14.43, 14.43]}

Asymptotes: slant

y-intercept

#### Explanation:

Resolving into partial fractions,

Rearranging.

The form reveals that the asymptotes are given by

the slant

Easily from the given equation, the intercepts can be obtained, as

given in the answer.

Also, as #x to +-oo, y to +-oo, observing that the second fraction

tends to 0.