How do you find the end behavior of f (x) = 3x^4 - 5x + 1?

Jul 4, 2017

See the explanation below.

Explanation:

First, graph the function.
graph{3x^4-5x+1 [-10, 10, -5, 5]}

Based on the graph, you can see that as $x \to \infty$, $f \left(x\right) \to \infty$.
As $x \to - \infty$, $f \left(x\right) \to \infty$.

You can also write this using limits:

${\lim}_{x \to \infty} f \left(x\right) = \infty$

${\lim}_{x \to - \infty} f \left(x\right) = \infty$