End Behavior of Polynomials

Front

What is the end behavior of a polynomial function?

Back

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

Front

What does x → ∞ indicate in terms of end behavior?

Back

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

Front

What does x → -∞ indicate in terms of end behavior?

Back

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

Front

How do you determine the end behavior of a polynomial function?

Back

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

Front

What is the significance of the leading coefficient in determining end behavior?

Back

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

Front

If the leading term of a polynomial is positive and of even degree, what is the end behavior?

Back

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

Front

If the leading term of a polynomial is negative and of even degree, what is the end behavior?

Back

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

Front

If the leading term of a polynomial is positive and of odd degree, what is the end behavior?

Back

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

Front

If the leading term of a polynomial is negative and of odd degree, what is the end behavior?

Back

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

Front

What does it mean if a polynomial function approaches -∞ as x approaches +∞?

Back

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