# End Behavior

## Key Questions

The end behavior of a function is the behavior of the graph of the function $f \left(x\right)$ as $x$ approaches positive infinity or negative infinity.

#### Explanation:

The end behavior of a function is the behavior of the graph of the function $f \left(x\right)$ as $x$ approaches positive infinity or negative infinity.

This is determined by the degree and the leading coefficient of a polynomial function.

For example in case of $y = f \left(x\right) = \frac{1}{x}$, as $x \to \pm \infty$, $f \left(x\right) \to 0$.
graph{1/x [-10, 10, -5, 5]}
But if $y = f \left(x\right) = \frac{3 {x}^{2} + 5}{\left(x + 2\right) \left(x + 7\right)}$ as $x \to \pm \infty$, $y \to 3$
graph{(3x^2+5)/((x+2)(x+7)) [-165.7, 154.3, -6, 12]}