Question

How do you find the end behavior of `x^3 + 3x + 2`?

Answer 1

The end behaviour will be determined by the term of highest degree. In this case we get:

`x^3+3x+2 -> +oo` as `x->+oo`

and

`x^3+3x+2 -> -oo` as `x->-oo`

Explanation:

The end behaviour will be determined by the term of highest degree - in this case `x^3`. Since the coefficient `1` is positive and the degree is odd, we get:

`x^3+3x+2 -> +oo` as `x->+oo`

and

`x^3+3x+2 -> -oo` as `x->-oo`

If the highest degree was even and the leading coefficient positive we would get `f(x)->+oo` as `x->+-oo`, etc.