Understanding End Behavior of Exponential Functions

TLDR; The video explains the end behavior of exponential functions, showing how the function values approach infinity or specific values as x approaches positive or negative infinity.

⏭️ End Behavior Definition

End behavior describes the value of the function as x approaches positive or negative infinity.

As x approaches positive infinity, the function values increase without bound, leading to the function approaching positive infinity.

Conversely, as x approaches negative infinity, the function values decrease without bound, and the function approaches a specific value.

📈 End Behavior of F of X = 3 x 2 to the Power of X - 10

As x approaches positive infinity, the function values increase without bound, causing the function to approach positive infinity.

Conversely, as x approaches negative infinity, the function approaches -10, leading to a horizontal asymptote of y = -10.

Graphical analysis supports these conclusions.

📊 End Behavior of F of X = -2 x 0.5 Raised to the Power of X + 5

As x approaches positive infinity, the function values approach positive 5, resulting in a horizontal asymptote of y = 5.

When x approaches negative infinity, the function approaches negative infinity, as supported by graphical analysis.

Analyzing the graph is recommended for confirming end behavior.

📉 Analyzing End Behavior

It's essential to analyze the graph to confirm the end behavior or long-run behavior of exponential functions.

Graphical analysis provides a clear visualization of how the function values behave as x approaches positive or negative infinity.

This analytical approach ensures a comprehensive understanding of the behavior.