End Behavior

Front

What is end behavior in mathematics?

Back

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

Front

What does it mean when we say a function approaches infinity as x approaches infinity?

Back

It means that the values of the function increase without bound as x increases.

Front

What does it mean when we say a function approaches negative infinity as x approaches negative infinity?

Back

It means that the values of the function decrease without bound as x decreases.

Front

If a function f(x) approaches infinity as x approaches infinity, what can we say about its end behavior?

Back

The end behavior indicates that the graph of the function rises indefinitely to the right.

Front

If a function f(x) approaches negative infinity as x approaches negative infinity, what can we say about its end behavior?

Back

The end behavior indicates that the graph of the function falls indefinitely to the left.

Front

What is the end behavior of f(x) if f(x) approaches infinity as x approaches -infinity?

Back

The graph of the function rises indefinitely to the left.

Front

What is the end behavior of f(x) if f(x) approaches negative infinity as x approaches infinity?

Back

The graph of the function falls indefinitely to the right.

Front

How can we determine the end behavior of polynomial functions?

Back

The end behavior of polynomial functions is determined by the leading term's degree and coefficient.

Front

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

Back

As x approaches both positive and negative infinity, f(x) approaches infinity.

Front

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

Back

As x approaches negative infinity, f(x) approaches negative infinity, and as x approaches positive infinity, f(x) approaches infinity.