Recall the definition of an inverse function.

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ecall the definition of an inverse function. Write the inverse Isolate y variable Math 30-1 1 1 Understanding Logarithms () y fx () x f y 2 1 y x 2 1 x y 1 2 x y 2 x y 2 y x 2 log y x 1 () y f x

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8.1 Understanding Logarithms. Recall the definition of an inverse function. Write the inverse. Isolate y variable. Graphing Logarithmic Functions. The logarithm function is the inverse of an exponential function. What is Log?. y = 2 x. 2. 4. 8. 1. 16. 2. 4. 8. 1. 16. - PowerPoint PPT Presentation

Transcript of Recall the definition of an inverse function.

PowerPoint Presentation

Recall the definition of an inverse function.

Write the inverse

Isolate y variable

Math 30-118.1 Understanding Logarithms

The logarithm function is the inverse of an exponential function.

124816

124816y = 2xy = log2x(x = 2y)

Change of base formula:

Graphing Logarithmic FunctionsMath 30-12

What is Log?2

xlog2xy0log201log212log224log248log28

Math 30-13Vertical Asymptote at x = 0The y-intercept is 1.There is no x-intercept.The domain is {x | x R}.The range is {y | y > 0}.There is a horizontal asymptoteat y = 0.There is no y-intercept.The x-intercept is 1.The domain is {x | x > 0}.The range is {y | y R}.There is a vertical asymptoteat x = 0.y = 2xy = log2xThe graph of y = 2x has been reflected in the line of y = x, to give the graph of y = log2x.Comparing Exponential and Logarithmic Function Graphs

Math 30-144

y = 2xy = xy = log2xGraphing the Logarithmic Function

Math 30-155Math 30-16

Base is

xlog2xy0log301log313log339log39

Vertical Asymptote at

Math 30-17Characteristics of the Graphs of Logarithmic Functions of the Form f(x) = logbxThe x-intercept is 1. There is no y-intercept.The y-axis is a vertical asymptote. (x = 0)If 0 < b < 1, the function is decreasing. If b > 1, the function is increasing. The graph is smooth and continuous. It has no sharp corners or edges.-2-1623455432-1-26f (x) = logb xb>1 -2-1623455432-1-26f (x) = logb x0


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