End Behavior

Front

What is end behavior in the context of functions?

Back

End behavior describes the behavior of a function as the input values (x) approach positive or negative infinity.

Front

What does it mean when we say a function's end behavior is 'down and down'?

Back

It means that as x approaches both negative infinity and positive infinity, the function's output (y) approaches negative infinity.

Front

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

Back

The end behavior of a polynomial function can be determined by the leading term's degree and its leading coefficient.

Front

What is the end behavior of the function y = x^2?

Back

As x → -∞, y → ∞ and as x → ∞, y → ∞.

Front

What is the end behavior of the function y = -x^2?

Back

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

Front

What does it indicate if a function's end behavior is 'up and up'?

Back

It indicates that as x approaches both negative infinity and positive infinity, the function's output (y) approaches positive infinity.

Front

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

Back

The leading coefficient determines whether the end behavior of the function will rise or fall as x approaches infinity or negative infinity.

Front

What is the end behavior of the function y = x^3?

Back

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

Front

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

Back

Even-degree polynomials have the same end behavior on both sides, while odd-degree polynomials have opposite end behaviors.

Front

What is the end behavior of the function y = -2x^3?

Back

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