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1 An example of an exponential function is:____________________________ What would the inverse of that function look like? Now we need to solve for y. In order to change x b y to proper form, new terminology had to be created by mathematicians. Therefore the word ________________________ is used in place of exponent. Exponential Form Logarithmic Form Graphing Sketch y 2x Sketch the inverse of y 2x y y x x
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2 y 2 x and ___________________ are inverses. x 2 y is equal to __________________, therefore, this is the graph of a logarithmic function. Graph (hint: convert to exponential form first) f ( x) log3 x f ( x) log 1 x 2 y y x x Characteristics: Domain:__________________________ Range:____________________________ ________________________ function Common point: _____________ therefore, the x intercept would be __________. There is not a ____________. Therefore there is a vertical asymptote at ________ If b > 1, the function is ___________________ If 0 < b < 1, the function is ________________
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3 Sketch: f ( x) log 4 (3 x) Hint: if you are using a table of values convert to exponential form first (switch and factor). x f(x) y x Interchanging Log and Exponential Forms Log Form Exponential Form log5 25 2 Remember that y log a x Evaluate: 1. y log9 27 hint: convert to exponential form and solve
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4 3 2. log b 4 3. log 2 (log3 9) x FYI: Logs which are to the base of 10 are called __________________________ Calculators are set up to deal with base 10 logs. It is often written without the “10” (x = log y) Evaluate: log10 100 Without Calculator With Calculator
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5 Transformations: State how each of the equations below transforms the graph of f ( x) loga x 1) f ( x) log2 ( x 1) 2) f ( x) log3 ( x 5) 3) f ( x) log 4 ( x) 3 4) f ( x) log5 ( x) 2 5) f ( x) log3 (1 x) 6) f ( x) log 2 (4 x) 1 7) f ( x) log 4 (3 x) On Your Own Sketch f ( x) log 4 (3 x) **Remember to change it to exponential form first! 4y x 4y x 3 y x y x y x
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6 On Your Own Sketch f ( x) log 2 ( x 1) 3 **Remember to change it to exponential form first! y x
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