Graph each exponential function. f(x)=2^-x

Name: Problem 46, Chapter 11: Intermediate Algebra
Uploaded: 2022-03-15T02:34:08-08:00
Duration: 1 min 10 s
Channel: Victor Salazar
Description: Graph each exponential function. f(x)=2^-x

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Key Concepts

Exponential Functions

An exponential function is a mathematical expression where a constant base is raised to a variable exponent, typically represented as f(x) = a^(x). These functions are foundational in understanding concepts of continuous growth or decay and are prevalent in various scientific, economic, and engineering contexts.

Graph Transformations

Graph transformations involve modifying the basic graph of a function through operations such as translations, reflections, scaling, and rotations. Understanding these helps in predicting how changes in the function’s formula affect its graph.

Reflection Across the Y-axis

When the exponent in an exponential function is negated, as in f(x) = 2^(-x), it results in a reflection of the graph over the y-axis. This transformation switches the direction of the function’s growth, turning a normally increasing exponential function into a decreasing one.

Domain, Range, and Asymptotic Behavior

Exponential functions generally have a domain of all real numbers and a range of positive numbers. They often exhibit an asymptote, typically the x-axis, which the graph approaches but never touches. Recognizing these attributes is crucial for accurate graphing and understanding their long-term behavior.

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