FIGURE N2–6DEFINITION
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
(a) f (x) = x^3 − 3x^2 + 7x + 2
SOLUTION:
(b) g(x) = −4x^4 + 1,000,000x^3 + 100
SOLUTION:
(c) h(x) = −5x^3 + 3x^2 −4π + 8
SOLUTION:
(d) k(x) = π − 0.001x
SOLUTION:
It’s easy to write rules for the behavior of a polynomial as x becomes infinite!