End Behavior of Exponential Functions

Front

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

Back

As x → ∞, y approaches a constant value (e.g., 2).

Front

What does it mean if the end behavior of a function is x → -∞, y → ∞?

Back

It means the function goes up on the left side.

Front

How can you determine if the function y = A * B^x is a growth model?

Back

The function is a growth model if B > 1.

Front

What does it indicate if the end behavior of a function is x → -∞, y → -∞?

Back

It means the function goes down on the left side.

Front

What is the end behavior of an exponential function on the left side?

Back

As x → -∞, y approaches 0.

Front

What is the general form of an exponential function?

Back

The general form is y = A * B^x, where A is a constant and B is the base.

Front

What is the significance of the base B in an exponential function?

Back

The base B determines the growth or decay of the function; if B > 1, it grows; if 0 < B < 1, it decays.

Front

What happens to the value of y in an exponential function as x approaches negative infinity?

Back

As x approaches -∞, y approaches 0 for growth functions.

Front

What is the end behavior of the function y = 2 * 3^x as x approaches infinity?

Back

As x → ∞, y → ∞.

Front

How does the value of A affect the graph of an exponential function?

Back

The value of A affects the vertical stretch or compression and the direction of the graph (upward or downward).