Question

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

Answer 1

The end behaviour of a polynomial function is determined by the term of highest degree, in this case `x^3`.

Hence `f(x)->+oo` as `x->+oo` and `f(x)->-oo` as `x->-oo`.

Explanation:

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(x)->+oo` as `x->+oo` and `f(x)->-oo` as `x->-oo`.