(a)

(b)

`Figure N2–6`

###### Definition

The theorems that follow in §C of this chapter confirm the conjectures made

about limits of functions from their graphs.

Finally, if the function f(x) becomes infinite as x becomes infinite, then one or

more of the following may hold:

###### End Behavior of Polynomials

Every polynomial whose degree is greater than or equal to 1 becomes infinite as

x does. It becomes positively or negatively infinite, depending only on the sign

of the leading coefficient and the degree of the polynomial.

###### Example 7 **__**

**__**For each function given below, describe .

`f (x) = x^3 − 3x^2 + 7 x + 2`

SOLUTION:.

`g(x) = −4x^4 + 1,000,000x^3 + 100`

SOLUTION:.