# How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given y=x^3-4x?

Jul 5, 2017

See the explanation below.

#### Explanation:

First, graph the function $f \left(x\right) = {x}^{3} - 4 x$.
graph{x^3-4x [-10, 10, -5, 5]}

From the graph, you can see 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:

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

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

There are 3 $x$-intercepts here because there are 3 points where the graph intercepts the $x$-axis.

Similarly, you can find the $y$-intercept graphically if you find the point where the graph intercepts the $y$-axis. In this case, the $y$-intercept is 0.

If you want to find the $y$-intercept algebraically, substitute 0 in for x.

$y = {x}^{3} - 4 x$
$y = {0}^{3} - 4 \left(0\right)$
$y = 0$