Sketch the graph of f(x)=2^-x.

Name: Problem 11, Chapter 7: Mathematics for Health Sciences: A Comprehensive Approach
Uploaded: 2020-10-22T03:58:42-08:00
Duration: 28 s
Channel: Harmender Singh Yadav
Description: Sketch the graph of f(x)=2^-x.

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Key Concepts

Horizontal Asymptote

A horizontal asymptote is a line that the graph of a function approaches as x tends to positive or negative infinity. For exponential functions with a base greater than one, such as f(x) = 2^x, the x-axis (y = 0) serves as the horizontal asymptote, indicating that while the function's values become very small for large negative x, they never actually reach zero.

Graphical Characteristics

The graph of an exponential function, especially when the base is greater than one, exhibits a continuously increasing curve. It has a domain of all real numbers and a range of positive real numbers, meaning it never touches the x-axis. The point where x equals zero always maps to 1, providing a clear y-intercept, while the curve approaches but does not meet the x-axis, which acts as a horizontal asymptote.

Exponential Functions

Exponential functions are mathematical functions in which the variable appears in the exponent. They are defined by the form f(x) = a^x where the base 'a' is a positive constant. These functions are key in modeling phenomena involving rapid growth or decay, and their behavior is distinctively different from linear or polynomial functions.

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