End Behavior

Front

What is end behavior in the context of polynomial functions?

Back

End behavior describes 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 role does the leading coefficient play in determining end behavior?

Back

The sign of the leading coefficient (positive or negative) influences whether the ends of the graph rise or fall.

Front

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

Back

As x → ∞, y → ∞ and as x → -∞, y → ∞.

Front

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

Back

As x → ∞, y → -∞ and as x → -∞, y → -∞.

Front

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

Back

As x → ∞, y → ∞ and as x → -∞, y → -∞.

Front

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

Back

As x → ∞, y → -∞ and as x → -∞, y → ∞.

Front

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

Back

As x → ∞, y → ∞ and as x → -∞, y → ∞.

Front

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

Back

As x → ∞, y → -∞ and as x → -∞, y → ∞.

Front

If a polynomial has a leading coefficient of -2 and degree 5, what is its end behavior?

Back

As x → ∞, y → -∞ and as x → -∞, y → ∞.