3.3 graphs of exponential functions
Transcript of 3.3 graphs of exponential functions
![Page 1: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/1.jpg)
3.3 Graphs of Exponential Functions
![Page 2: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/2.jpg)
Exponential Growth Graphs•When b > 1 ▫ graph moves away from x-axis quickly from left to right.
•y-intercept is at point (0, a).
![Page 3: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/3.jpg)
Exponential Decay Graphs•When 0< b < 1 ▫ graph moves towards x-axis quickly from left to right.
•y-intercept is at point (0, a).
![Page 4: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/4.jpg)
Asymptotes•An asymptote is a line that a graph approaches (but does not touch) as it moves away from the origin.
•Functions of the formy = a(b)x have horizontal asymptotes at y = 0.
![Page 5: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/5.jpg)
Domain & Range•Domain & Range describe which input/output values will work for a given function.•Domain – set of all input values (x’s)▫Look left and right•Range – set of all output values (y’s)▫Look up and down•Can be written using inequalities.
![Page 6: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/6.jpg)
Example 1:•Identify the following -
•Growth or Decay?
•Domain:
•Range:
•Asymptote:
•y-int:
![Page 7: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/7.jpg)
Example 2:•Identify the following -
•Growth or Decay?
•Domain:
•Range:
•Asymptote:
•y-int:
![Page 8: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/8.jpg)
You Try!•Identify the following -
•Growth or Decay?
•Domain:
•Range:
•Asymptote:
•y-int:
![Page 9: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/9.jpg)
Graphing Exponential Functions•To graph y = a(b)x 1. Make a table2. Plot the points3. Connect with a smooth curve
Be Careful:• Don’t cross the asymptote (y = 0)!!• Check that y-int is (0, a)!!
![Page 10: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/10.jpg)
Example 1:•Graph •State the domain and range.
![Page 11: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/11.jpg)
Example 2:•Graph •State the domain and range.
![Page 12: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/12.jpg)
You Try!
•Graph •State the domain and range.
![Page 13: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/13.jpg)
Example 3:•Graph •State the domain and range.
![Page 14: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/14.jpg)
Example 4:•Graph •State the domain and range.
![Page 15: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/15.jpg)
You Try!•Graph •State the domain and range.
![Page 16: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/16.jpg)
Transformations •Remember: •+ and – mean shift•Changing the input shifts left/right▫Do the opposite!!•Changing the output shifts up/down
•We will call the original function y = a(b)x the “parent function”•Its graph is the “parent graph”
![Page 17: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/17.jpg)
Example 1:•Identify the parent function and describe the transformation on it.
1.
2.
3.
![Page 18: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/18.jpg)
You Try!•Identify the parent function and describe the transformation on it.
1.
2.
3.
![Page 19: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/19.jpg)
To Graph:•Sketch the parent graph with a dashed line.•Shift points and draw final graph. •Example:•Graph •Domain:•Range:
![Page 20: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/20.jpg)
Example 2:
•Graph
•Domain:•Range:
![Page 21: 3.3 graphs of exponential functions](https://reader036.fdocuments.us/reader036/viewer/2022062308/55895cffd8b42a693f8b461d/html5/thumbnails/21.jpg)
You Try!
•Graph
•Domain: •Range: