# Asymptote Calculator

## Find asymptotes step by step

The calculator will try to find the vertical, horizontal, and slant asymptotes of the function, with steps shown.

### Solution

**Your input: find the vertical, horizontal and slant asymptotes of the function $$$f(x)=x^{4} - 6 x^{2}$$$**

### Vertical Asymptotes

The line $$$x=L$$$ is a vertical asymptote of the function $$$y=x^{4} - 6 x^{2}$$$, if the limit of the function (one-sided) at this point is infinite.

In other words, it means that possible points are points where the denominator equals $$$0$$$ or doesn't exist.

So, find the points where the denominator equals $$$0$$$ and check them.

As can be seen, there are no such points, so this function doesn't have vertical asymptotes.

### Horizontal Asymptotes

Line $$$y=L$$$ is a horizontal asymptote of the function $$$y=f{\left(x \right)}$$$, if either $$$\lim_{x \to \infty} f{\left(x \right)}=L$$$ or $$$\lim_{x \to -\infty} f{\left(x \right)}=L$$$, and $$$L$$$ is finite.

Calculate the limits:

$$$\lim_{x \to \infty}\left(x^{4} - 6 x^{2}\right)=\infty$$$ (for steps, see limit calculator).

$$$\lim_{x \to -\infty}\left(x^{4} - 6 x^{2}\right)=\infty$$$ (for steps, see limit calculator).

Thus, there are no horizontal asymptotes.

### Slant Asymptotes

Since the degree of the numerator is not one degree greater than the denominator, then there are no slant asymptotes.

**Answer**

**No vertical asymptotes.**

**No horizontal asymptotes.**

**No slant asymptotes.**