End Behavior - Polynomials

Front

What is end behavior in the context of polynomial functions?

Back

End behavior refers to the behavior of the graph of a polynomial function as x approaches positive or negative infinity.

Front

How does the degree of a polynomial affect its end behavior?

Back

The degree of a polynomial determines the direction in which the graph rises or falls as x approaches infinity or negative infinity.

Front

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

Back

The leading coefficient indicates whether the ends of the graph will rise or fall. A positive leading coefficient means the graph rises to the right, while a negative leading coefficient means it falls to the right.

Front

Describe the end behavior of a polynomial function with an even degree and a positive leading coefficient.

Back

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

Front

Describe the end behavior of a polynomial function with an even degree and a negative leading coefficient.

Back

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

Front

Describe the end behavior of a polynomial function with an odd degree and a positive leading coefficient.

Back

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

Front

Describe the end behavior of a polynomial function with an odd degree and a negative leading coefficient.

Back

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

Front

What is the end behavior of the polynomial f(x) = 2x^4 - 3x + 1?

Back

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

Front

What is the end behavior of the polynomial f(x) = -x^3 + 4x - 2?

Back

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

Front

How can you determine the end behavior of a polynomial function from its graph?

Back

By observing the direction in which the graph approaches as x moves towards positive and negative infinity.