4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.
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Transcript of 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.
![Page 1: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/1.jpg)
4.3 Logarithmic Functions and Graphs
Do NowFind the inverse of f(x) = 4x^2 - 1
![Page 2: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/2.jpg)
Logarithmic Functions
• A logarithmic function is the inverse of an exponential function
• It behaves similarly to an exponential function
![Page 3: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/3.jpg)
Logarithmic Functions as an Inverse
• The inverse of is given by
• We convert between the 2 equations when evaluating logarithms
![Page 4: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/4.jpg)
Ex
• Find each of the following:• 1)• 2)• 3)• 4)• 5)• 6)
![Page 5: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/5.jpg)
Ex
• Convert each of the following to a logarithmic equation
• 1)
• 2)
• 3)
![Page 6: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/6.jpg)
Ex
• Convert to an exponential equation• 1)
• 2)
• 3)
![Page 7: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/7.jpg)
Logarithms and Calculators
• Logarithms can be evaluated on calculators– We can evaluate base 10 (LOG) and base e (LN)
logarithms using our calculators
• To convert logarithms, we need to use the change of base formula
![Page 8: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/8.jpg)
Changing Logarithmic Bases
• For any logarithmic bases a and b, and any positive number M,
![Page 9: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/9.jpg)
Ex
• Evaluate using the change of base formula
![Page 10: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/10.jpg)
Closure
• Evaluate without a calculator
• HW: p.387 #9-77 odds
![Page 11: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/11.jpg)
4.3 Logarithmic GraphsWed April 8
• Do Now• Evaluate the following without a calculator• 1)
• 2)
![Page 12: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/12.jpg)
HW Review: p.387 #9-77
![Page 13: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/13.jpg)
Graphs of Logarithmic Functions
• Since logarithms are inverses of exponential functions, the following are true:– The x-intercept is (1,0)– There is a vertical asymptote at x = 0– The domain is all positive numbers– The range is all real numbers
If you want to graph on the calculator, you must use the change of base formula and graph that
![Page 14: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/14.jpg)
Ex
• Graph
![Page 15: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/15.jpg)
Ex• Graph each of the following. Describe how
each graph can be obtained from the basic function graph
• 1)
• 2)
• 3)
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Applications
• Ex 12 and 13 in book p.384
![Page 17: 4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649db25503460f94aa212c/html5/thumbnails/17.jpg)
Closure
• Graph
• HW: p.387 #79-97 odds