End Behavior of Polynomials

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity.

It indicates that as x approaches positive infinity, we are observing the behavior of the function in the right tail of the graph.

It indicates that as x approaches negative infinity, we are observing the behavior of the function in the left tail of the graph.

The end behavior can be determined by analyzing the leading term of the polynomial and its degree.

The leading coefficient determines whether the ends of the graph rise or fall as x approaches infinity or negative infinity.

As x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞.

As x → ∞, f(x) → -∞ and as x → -∞, f(x) → -∞.

As x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞.

As x → ∞, f(x) → -∞ and as x → -∞, f(x) → ∞.

It means that the right end of the graph falls downwards.