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Exponential Properties

Hexagon Integration Icon for exponential base graphs on Online Math Tutor, LLC

Exponent

Graphs

b is greater than 1
Hexagon Integration Icon for exponential base graphs on Online Math Tutor, LLC

Exponent

Graphs

b is postive and less than 1

Basics Facts:

Function: \(f(x)=b^x\)

Restriction: \( 0<b,\, b\neq1\)

Domain: \((-\infty, \infty)\)

Range: \((0, \infty)\)

Intercept: \((0,1)\)

Horizontal Asymptote: x-axis, \(\)y=0\(\)

Addition Property

Power Property

Difference Property

Zero Property

Product Property

Product of a Power

Quotient of a Power 

Radical Property

Various Properties of Negative Exponents

Logarithmic Properties

If \(b^x=y\) then \(log_b(y)=x\)

Hexagon Integration Icon for logarithmic base graphs on Online Math Tutor, LLC

Logarithms

Graphs

b is greater than 1
Hexagon Integration Icon for logarithmic base graphs on Online Math Tutor, LLC

Logarithms

Graphs

b is postive and less than 1

Basics Facts:

Function: \(f(x)=log_{b}(x)\)

Restriction: \( 0<b,\, b\neq1\)

Domain: \((0, \infty)\)

Range: \((-\infty,\infty)\)

Intercept: \((1,0)\)

Vertical Asymptote: y-axis, \(x=0\)

Identity

Identity

Product Property

Quotient Property

Exponentiation Property

Power Property

Common  Logarithm

Natural Logarithm

Change of Base
[Natural Logarithm]