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 graph has end behavior of x → ∞, y → ∞ and x → -∞, y → -∞?

Back

It indicates that the graph rises indefinitely on both ends.

Front

What does it indicate if a graph has end behavior of x → ∞, y → -∞ and x → -∞, y → -∞?

Back

It indicates that the graph falls indefinitely on the right side and also falls indefinitely on the left side.

Front

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

Back

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

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) → ∞.

Front

What does it mean if a function's end behavior is described as x → ∞, y → 0?

Back

It means that as x increases indefinitely, the function approaches a horizontal line (y = 0) but does not cross it.