Laws of the End Behavior of a Polynomial Function
End Behavior of
Polynomial Functions:
The characteristic of a continuous function at extreme points.
Polynomial Function Expression:
anxn+an-1xn-1+an-2xn-2… +a2x2+a1x1+a0
anxn+an-1xn-1+an-2xn-2… +a2x2+a1x1+a0
Odd Exponents (n):
When the leading
coefficient is positive (an>0), the graph falls to the left and
rises to the right:
f(x) → ∞
as x → ∞
&
f(x) → -∞
as x → -∞
When the leading
coefficient is negative (an<0), the graph rises to the left and
falls to the rights.
f(x) → ∞
as x → -∞
&
f(x) → -∞
as x → ∞
Even Exponents (n):
When the leading
coefficient is positive (an>0), the graph rises to the left
and right.
f(x) → ∞
as x → -∞
&
f(x) → ∞
as x → ∞
When the leading
coefficient is negative (an<0), the graph falls to the left
and right.
f(x) → -∞
as x → -∞
&
f(x) → -∞
as x → ∞
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