End Behavior

Front

What is end behavior in the context of graphing functions?

Back

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

Front

As x approaches -∞, what does it mean if f(x) approaches -∞?

Back

It means that the graph of the function falls indefinitely as x moves towards negative infinity.

Front

As x approaches +∞, what does it mean if f(x) approaches +∞?

Back

It means that the graph of the function rises indefinitely as x moves towards positive infinity.

Front

What does it indicate if a function's end behavior is f(x) → -∞ as x → -∞ and f(x) → +∞ as x → +∞?

Back

This indicates that the graph falls to negative infinity on the left and rises to positive infinity on the right.

Front

What is the significance of identifying end behavior in a graph?

Back

Identifying end behavior helps in understanding the overall trend of the function and predicting its behavior outside the visible range.

Front

If a graph has end behavior f(x) → +∞ as x → -∞ and f(x) → +∞ as x → +∞, what does this suggest about the function?

Back

This suggests that the function rises on both ends, indicating a possible minimum point in the middle.

Front

What does it mean if a function's end behavior is f(x) → 0 as x → +∞?

Back

It means that as x increases indefinitely, the function approaches a horizontal asymptote at y = 0.

Front

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

Back

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

Front

What is the end behavior of a quadratic function with a positive leading coefficient?

Back

As x → -∞, f(x) → +∞ and as x → +∞, f(x) → +∞.

Front

What is the end behavior of a cubic function with a negative leading coefficient?

Back

As x → -∞, f(x) → +∞ and as x → +∞, f(x) → -∞.