Question

What does a function's end behavior mean?

Answer 1

The end behavior of a function is the behavior of the graph of the function `f(x)` 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(x)` 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(x)=1/x`, as `x->+-oo`, `f(x)->0`.
graph{1/x [-10, 10, -5, 5]}
But if `y=f(x)=(3x^2+5)/((x+2)(x+7))` as `x->+-oo`, `y->3`
graph{(3x^2+5)/((x+2)(x+7)) [-165.7, 154.3, -6, 12]}