# How do you describe the end behavior for f(x)=x^4-3x^2-3x+4?

As $x \to \infty , f \left(x\right) \to \infty$
As $x \to - \infty , f \left(x\right) \to \infty$
When working with end behavior, look at the leading term (term with highest exponent) and neglect all other terms, in this case ${x}^{4}$ is the leading term.
If $x$ is a very large positive number ($\infty$), ${x}^{4}$ will be a very large positive number ($\infty$) also, and if $x$ is a very-large-in-magnitude negative number ($- \infty$), ${x}^{4}$ will be a large "positive" number ($\infty$) because of the even power "$4$".