Question

Find the vertical, horizontal, and oblique asymptotes, if any, for the given rational function.

Answer 1

Answer:

Polynomial functions of degree 1 or higher can't have asymptotes.

Therefore, the function $g\left(x\right)=3x^4\:-\:3x$ does not have any Asymptotes.

The graph is also attached below.

Step-by-step explanation:

Given the function

$g\left(x\right)=3x^4\:-\:3x$

Determining the Asymptotes

Vertical Asymptotes:

Polynomial functions of degree 1 or higher can't have asymptotes.

so

There are No vertical asymptotes.

Horizontal Asymptotes:

As we already know that Polynomial functions of degree 1 or higher can't have asymptotes.

so

There are NO horizontal Asymptotes.

Therefore, the function $g\left(x\right)=3x^4\:-\:3x$ does not have any Asymptotes.

The graph is also attached below.