# How do you find the end behavior of f(x)= -x^4+x^2?

$f \left(x\right) \to - \setminus \infty$ as $x \to \setminus \pm \setminus \infty$
The function $f \left(x\right) = - {x}^{4} + {x}^{2}$ is a polynomial with a degree of 4 (the largest exponent), which is even. Also, the coefficient of the highest powered term is negative.
These facts are enough to conclude that $f \left(x\right) \to - \setminus \infty$ as $x \to \setminus \pm \setminus \infty$. This means that the graph of $f$ goes down forever and ever without bound as $| x |$ gets larger and larger without bound. To be a bit more precise, the graph of $f$ will go below and stay below any given horizontal line by choosing $x$ to be sufficiently far from zero.