End Behavior of Exponential Functions

Front

What is the end behavior of an exponential function as x approaches negative infinity?

Back

As x approaches -∞, the function approaches 0 (y → 0).

Front

What does the variable y represent in the context of exponential functions?

Back

The variable y represents the output of the function, indicating the value of the function at a given x.

Front

What does the variable x represent in the context of exponential functions?

Back

The variable x represents the input of the function, indicating the value at which the function is evaluated.

Front

What is the end behavior of an exponential function as x approaches positive infinity?

Back

As x approaches +∞, the function approaches infinity (y → ∞).

Front

What does it mean if a function goes up on the left?

Back

It means that as x approaches -∞, y approaches ∞ (x → -∞, y → ∞).

Front

What does it mean if a function goes down on the left?

Back

It means that as x approaches -∞, y approaches -∞ (x → -∞, y → -∞).

Front

In the context of exponential functions, what does y → ∞ indicate?

Back

It indicates that the function's output increases without bound as x increases.

Front

In the context of exponential functions, what does y → -∞ indicate?

Back

It indicates that the function's output decreases without bound as x increases.

Front

What is the general shape of an exponential function?

Back

Exponential functions typically have a J-shaped curve, increasing rapidly for positive x and approaching zero for negative x.

Front

How does the base of an exponential function affect its end behavior?

Back

A larger base results in a steeper increase as x approaches +∞, while a base between 0 and 1 results in a decrease.