Graphing Exponential Functions: Example 1

This section demonstrates the process of graphing f(x) = 2ˣ through a systematic approach using value tables and point plotting.

Example: For f(x) = 2ˣ, plotting points from x = -2 to x = 2 reveals the characteristic exponential growth curve.

Highlight: The graph approaches but never touches the x-axis as x decreases, creating a horizontal asymptote at y = 0.

Definition: A horizontal asymptote is a horizontal line that the graph approaches but never reaches.

Introduction to Exponential Functions

This opening section provides a foundational understanding of exponential functions in mathematics and applications. The content explains the basic structure and importance of these functions in real-world scenarios.

Definition: An exponential function is expressed as f(x) = bˣ, where b is the base (b > 0 and b ≠ 1) and x is the variable in the exponent.

Example: Common exponential functions include f(x) = 2ˣ, f(x) = 5ˣ⁻², and f(x) = 9²ˣ⁺¹.

Highlight: These functions are particularly relevant in financial applications, including credit cards, bank accounts, and loans.

Vocabulary: The domain of an exponential function encompasses all real numbers, making it extremely versatile for various applications.