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Chapter 4 - Functions

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Exponential Functions


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Functions - Exponential Functions - Contents

The exponential function has the form y equals e to the power of x. This special equation is the inverse function of the natural logarithmic function. There are other general exponential functions that have the form y equals n to the power of x, where the base number n is a numeric constant, for instance, two to the power of x. These functions are similar to the power function. If it is not specified the exponential function refers to the equation using the special number e as a base number. If n is a common fraction then the numerator is taken to the power and the denominator is taken to the power. The domain of the exponential function is the set of all real numbers. The number n is normally a positive number and then the range of the function is restricted to positive numbers, since all powers of a positive number are positive.

Functions - Exponential Functions - Examples

The exponential function:
y
=
e to the power of x,

when x = 1 then y = e
.

The natural logarithm is the inverse function:
y
= ln(x),
when x = e then y = 1.

Functions - Exponential Functions - Mysteries

Math Mysteries: The exponential function increases so rapidly that when something multiplies fast it is said to be increasing exponentially. If y equals two to the power of x, as x increases incrementally from one, y is equal to 2, 4, 8, 16, 32, 64, 128, 256 512, 1024 . . . These numbers may be recognized from the binary system used in computers.

Functions - Sections - Chapters
1 - Function Definition 2 - Function Notation 3 - Function Domain
4 - Function Range 5 - Composite Functions 6 - Inverse Functions
7 - Linear Functions 8 - Power Functions 9 - Quadratic Functions
10 - Logarithmic Functions 11 - Exponential Functions 12 - Factorial Functions
13 - Limit Functions 14 - Summation Functions 15 - Percentage Functions

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