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

True or False: The end behavior of a polynomial function is determined by its leading term.

Back

True

Front

True or False: If the leading coefficient of a polynomial is positive and the degree is even, the end behavior will both approach positive infinity as x approaches both positive and negative infinity.

Back

True

Front

True or False: The end behavior of a function can be different for positive and negative infinity.

Back

True

Front

True or False: A function can have the same end behavior at both ends of the graph.

Back

True

Front

As x approaches -∞, if f(x) approaches +∞, what can be said about the leading coefficient and degree of the function?

Back

The leading coefficient is negative and the degree is odd.

Front

As x approaches +∞, if f(x) approaches -∞, what can be said about the leading coefficient and degree of the function?

Back

The leading coefficient is positive and the degree is odd.

Front

What is the end behavior of the function f(x) = 2x^2 + 3 as x approaches ±∞?

Back

As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches +∞.

Front

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

Back

The degree determines whether the ends of the graph go in the same direction (even degree) or opposite directions (odd degree).

Front

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

Back

As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches -∞.