End Behavior of Polynomial Functions

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:
a_nxⁿ+a_n-1x^n-1+a_n-2x^n-2… +a₂x²+a₁x¹+a₀

Odd Exponents (n): 

When the leading coefficient is positive (a_n>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 (a_n<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 (a_n>0), the graph rises to the left and right.

f(x) → ∞ 

as x → -∞

&

f(x) → ∞ 

as x → ∞

When the leading coefficient is negative (a_n<0), the graph falls to the left and right.

f(x) → -∞ 

as x → -∞

&

f(x) → -∞ 

as x → ∞