Graphs of One-to-One Functions In the following graphs of one-to-one functions, draw a horizontal...
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Transcript of Graphs of One-to-One Functions In the following graphs of one-to-one functions, draw a horizontal...
![Page 1: Graphs of One-to-One Functions In the following graphs of one-to-one functions, draw a horizontal line through more than one point on the graph if possible.](https://reader035.fdocuments.net/reader035/viewer/2022072011/56649de85503460f94ae2123/html5/thumbnails/1.jpg)
Graphs of One-to-One Functions
In the following graphs of one-to-one functions, draw a horizontalline through more than one point on the graph if possible.
Write a rule for determining a one-to-one function from a graph of afunction by drawing a horizontal line through points on the graph.
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1. 2.
Chapter 14Discovery 1
![Page 2: Graphs of One-to-One Functions In the following graphs of one-to-one functions, draw a horizontal line through more than one point on the graph if possible.](https://reader035.fdocuments.net/reader035/viewer/2022072011/56649de85503460f94ae2123/html5/thumbnails/2.jpg)
Graphs of One-on-One Functions
Check your rule on the following graph of a function, which is notone-to-one:
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3.
Chapter 14Discovery 1
![Page 3: Graphs of One-to-One Functions In the following graphs of one-to-one functions, draw a horizontal line through more than one point on the graph if possible.](https://reader035.fdocuments.net/reader035/viewer/2022072011/56649de85503460f94ae2123/html5/thumbnails/3.jpg)
Equivalent Exponential Functions
1. Graph each exponential function on a decimal window.
. ( ) 2 . ( ) 2
1 1. ( ) . ( )
2 2
a b
c d
x x
x x
f x f x
f x f x
2. Match the graphs of the functions.
Write a rule for determining equivalent functions.
Chapter 14Discovery 2
![Page 4: Graphs of One-to-One Functions In the following graphs of one-to-one functions, draw a horizontal line through more than one point on the graph if possible.](https://reader035.fdocuments.net/reader035/viewer/2022072011/56649de85503460f94ae2123/html5/thumbnails/4.jpg)
Effect of the Base a on an Exponential Graph
1. Sketch the graphs of the given exponential functions of the formf(x) = ax, where a > 0, on the same coordinate plane. Use the decimalwindow.
. ( ) 2 . ( ) 5 . ( ) 10
1 1 1. ( ) . ( ) . ( )
2 5 10
a b c
d e f
x x x
x x x
f x f x f x
f x f x f x
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Chapter 14Discovery 3
![Page 5: Graphs of One-to-One Functions In the following graphs of one-to-one functions, draw a horizontal line through more than one point on the graph if possible.](https://reader035.fdocuments.net/reader035/viewer/2022072011/56649de85503460f94ae2123/html5/thumbnails/5.jpg)
Effect of the Base a on an Exponential Graph
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Use your graphs to complete the following exercises:2. Determine the domain of each function.3. Determine the range for each function.4. Are all the functions one-to-one?5. Determine the y-intercept of each function.6. Determine the x-intercept of each function.
Choose the correct answer:7. In exercises 1a - 1c, a > 1. The function is increasing/decreasing. The larger the value of a, the steeper/shallower the graph.8. In exercises 1d -1f, 0 < a < 1. The function is increasing/decreasing.The smaller the value of a (as a approaches 0), the steeper/shallowerthe graph.
Chapter 14Discovery 3
![Page 6: Graphs of One-to-One Functions In the following graphs of one-to-one functions, draw a horizontal line through more than one point on the graph if possible.](https://reader035.fdocuments.net/reader035/viewer/2022072011/56649de85503460f94ae2123/html5/thumbnails/6.jpg)
Properties of Logarithms
Determine the following logarithms in the form logax:
3 5
3 5
2 2
3 5
3 5
3 5
. . log 1 . log 1
. . log 3 . log 5
. . log 3 . log 5
. . log 1 . log ( 1)
. . log 0 . log 0
1 a b
2 a b
3 a b
4 a b
5 a b
6. In exercise 1, x = 1. The logarithms are ____.7. In exercise 2, x = a, the base. The logarithms are ____.8. In exercise 3, x = a2, the base squared. The logarithms are ____.9. In exercise 4, x = -1. The logarithms are ____.10. In exercise 5, x = 0. The logarithms are ____.
Chapter 14Discovery 4
![Page 7: Graphs of One-to-One Functions In the following graphs of one-to-one functions, draw a horizontal line through more than one point on the graph if possible.](https://reader035.fdocuments.net/reader035/viewer/2022072011/56649de85503460f94ae2123/html5/thumbnails/7.jpg)
Product, Quotient, and Power Rulesof Logarithms
Approximate each expression, and compare the results obtained in theleft column with the corresponding results in the right column.
1. Product rule. log(3 4) . log3 log 4
. ln (2 5) . ln 2 ln5
a b
c d
2. Quotient rule3
. log . log3 log 44
2. ln . ln 2 ln5
5
a b
c d
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Chapter 14Discovery 5
![Page 8: Graphs of One-to-One Functions In the following graphs of one-to-one functions, draw a horizontal line through more than one point on the graph if possible.](https://reader035.fdocuments.net/reader035/viewer/2022072011/56649de85503460f94ae2123/html5/thumbnails/8.jpg)
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Product, Quotient, and Power Rulesof Logarithms
3. Power rule4
5
. log3 . 4log3
. ln 2 . 5 In 2
a b
c d
Write the following rules of logarithms:4. Product Rule:
5. Quotient Rule:
6. Power Rule:
Chapter 14Discovery 5
Approximate each expression, and compare the results obtained in theleft column with the corresponding results in the right column.
![Page 9: Graphs of One-to-One Functions In the following graphs of one-to-one functions, draw a horizontal line through more than one point on the graph if possible.](https://reader035.fdocuments.net/reader035/viewer/2022072011/56649de85503460f94ae2123/html5/thumbnails/9.jpg)
Properties of Exponential and Logarithms Equations
Complete the following statements with “true” or “false”:
1. a. If 2 = 2 is true, the 52 = 52 is ____. b. If 2 = 2 is true, then 122 = 122 is ____. c. If 2 = 2 is true, then e2 = e2 is ____.Write a rule for determining a true equation using exponentials.
2. a. If 2 = 2 is true, then log52 = log52 is ____. b. If 2 = 2 is true, then log122 = log122 is ____. c. If 2 = 2 is true, then ln 2 = ln 2 is ____.Write a rule for determining a true equation using logarithms.
Chapter 14Discovery 6