# How do you find the end behavior of x^3 + 3x + 2?

Jul 19, 2015

The end behaviour will be determined by the term of highest degree. In this case we get:

${x}^{3} + 3 x + 2 \to + \infty$ as $x \to + \infty$

and

${x}^{3} + 3 x + 2 \to - \infty$ as $x \to - \infty$

#### Explanation:

The end behaviour will be determined by the term of highest degree - in this case ${x}^{3}$. Since the coefficient $1$ is positive and the degree is odd, we get:

${x}^{3} + 3 x + 2 \to + \infty$ as $x \to + \infty$

and

${x}^{3} + 3 x + 2 \to - \infty$ as $x \to - \infty$

If the highest degree was even and the leading coefficient positive we would get $f \left(x\right) \to + \infty$ as $x \to \pm \infty$, etc.