# How do you find the end behavior of f(x) = x^6 + 2?

Jul 5, 2015

Observe that the highest order term is ${x}^{6}$. This will be the dominant term for large values of $x$. Since its coefficient is positive and its degree is even $f \left(x\right) \to + \infty$ as $x \to \pm \infty$
If the coefficient of the highest order term is positive and the degree is even then $f \left(x\right) \to + \infty$ as $x \to \pm \infty$.
If the coefficient of the highest order term is positive and the degree is odd then $f \left(x\right) \to + \infty$ as $x \to + \infty$ and $f \left(x\right) \to - \infty$ as $x \to - \infty$.