Wondershare MindMaster
Further Transcendental Function
6
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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.
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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)
