Mind Map Gallery Further Transcendental Function

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Release time：2020-10-08

Further Transcendental Function

In other words, a transcendental function "transcends" algebra in that it cannot be expressed in terms of a finite sequence of the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and root extraction.

Edited at 2020-10-08 09:13:20

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Further Transcendental Function

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Outline

Further-Transcendental-Functions

Logarithmic Functions

Properties of Logarithmic functions

Change of Base

Logarithmic Properties

Product Property

Quotient Property

Power Property

One to One Property

Solving Logarithmic functions

Expanding Logarithmic Functions (makethem longer)

Condensing Logarithmic Functions(make them shorter)

Check for Extraneous Solutions (makesure the solutions fall into thedomain)

Solving Using One to One Property (Ifall terms share a log and log base,then they cancel out)

Types of Logs

Natural Log (Ln)

Common Log (log)

Graphing

Graphing by Transformations

Horizontal Translation

Dilation

Reflection

Vertical Translation

Properties

X and Y Intercepts: (1,0) and None

Vertical Asymptote: x=0

End Behavior: As x approaches 0, yapproaches negative infinity. As xapproaches infinity, y approachesinfinity.

Domain and Range: (0 to infinity) and(negative infinity to infinity)

Key Points: 1,0 and b,1

Modeling with Nonlinear Regression

Use Regression to Solve

Predict (How long will it take? Howmany in soso years?)

Best Fit Equation (Which one is closerto 1.00)

Linearizing

Exponential Functions

Exponential Growth & Decay

Compound & Continuous Interest(Pe^rt and N=(1+r/n)^t)

Half Life (Pe^(.5)(t))

Solving Exponential Equations

Solving Using One to One Property (Ifterms share a base, then the basescancel and the exponents are equal toeach other)

Solving with Quadratic Equations(Factor and set the factors equal to0)

Graphing

Graphing by Transformations

Horizontal Translation

Dilation

Reflection

Vertical Asymptote

Properties

X and Y Intercept: None and (0,1)

End Behavior: As x approaches negativeinfinity, y approaches 0. As xapproaches infinity, y approachesinfinity.

Horizontal Asymptote: y=0

Domain and Range: (negative infinityto infinity) and (0 to infinity)

Key Points: (0,1) and (1,b)