# What is the end behavior of the function f(x) = x^3 + 2x^2 + 4x + 5?

The end behaviour of a polynomial function is determined by the term of highest degree, in this case ${x}^{3}$.
Hence $f \left(x\right) \to + \infty$ as $x \to + \infty$ and $f \left(x\right) \to - \infty$ as $x \to - \infty$.
For large values of $x$, the term of highest degree will be much larger than the other terms, which can effectively be ignored. Since the coefficient of ${x}^{3}$ is positive and its degree is odd, the end behaviour is $f \left(x\right) \to + \infty$ as $x \to + \infty$ and $f \left(x\right) \to - \infty$ as $x \to - \infty$.