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# Exercise #21

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### Transcript of "Exercise #21"

1. 1. 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
2. 2. 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 ________________
3. 3. 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
4. 4. 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
5. 5. 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
6. 6. 6 On Your Own Sketch f ( x) log 2 ( x 1) 3 **Remember to change it to exponential form first! y x