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 it mean when y → ∞?

Back

It means that the graph of the function rises indefinitely as x increases.

Front

What does it mean when y → -∞?

Back

It means that the graph of the function falls indefinitely as x increases.

Front

If a polynomial function has a positive leading coefficient and an even degree, what is its end behavior?

Back

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

Front

If a polynomial function has a negative leading coefficient and an odd degree, what is its end behavior?

Back

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

Front

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

Back

The leading coefficient determines the direction of the graph's ends based on its sign and the degree of the polynomial.

Front

How do you determine the end behavior from a graph?

Back

Look at the direction the graph is heading as x approaches positive and negative infinity.

Front

What is the end behavior of the function f(x) = x^3?

Back

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

Front

What is the end behavior of the function f(x) = -x^2?

Back

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

Front

What does it mean when a graph approaches a horizontal asymptote?

Back

It indicates that the function approaches a specific y-value as x approaches infinity or negative infinity.