End Behavior

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 the input values (x) approach positive or negative infinity.

Front

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

Back

The degree of a polynomial determines the number of times the graph can change direction, influencing whether the ends of the graph rise or fall.

Front

What role does the leading coefficient play in determining end behavior?

Back

The sign of the leading coefficient (positive or negative) indicates whether the graph rises or falls as x approaches positive or negative infinity.

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

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

What is the end behavior of the function f(x) = -2x^7 + 2x^4 + 4?

Back

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

Front

What is the end behavior of the function f(x) = 3x^5 - x^2 + 1?

Back

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

Front

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

Back

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

Front

What is 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

What is the end behavior of a polynomial function with an even degree and a negative leading coefficient?

Back

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