Warm-Up. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.
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Transcript of Warm-Up. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.
![Page 1: Warm-Up. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.](https://reader035.fdocuments.net/reader035/viewer/2022072010/56649dce5503460f94ac29b2/html5/thumbnails/1.jpg)
Warm-Up
Given , evaluate the following:
1.
2.
3.
4.
5.
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FUNCTIONSSymmetric about the y axis
Symmetric about the origin
![Page 3: Warm-Up. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.](https://reader035.fdocuments.net/reader035/viewer/2022072010/56649dce5503460f94ac29b2/html5/thumbnails/3.jpg)
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8
7
123456
8
-2-3-4-5-6-7
For an even function: for every point (x, y) on the graph, the point (-x, y) is also on the graph.
Even functions have y-axis Symmetry
![Page 4: Warm-Up. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.](https://reader035.fdocuments.net/reader035/viewer/2022072010/56649dce5503460f94ac29b2/html5/thumbnails/4.jpg)
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8
7
123456
8
-2-3-4-5-6-7
For an odd function: for every point (x, y) on the graph, the point (-x, -y) is also on the graph.
Odd functions have origin Symmetry
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2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8
7
123456
8
-2-3-4-5-6-7
We wouldn’t talk about a function with x-axis symmetry because it wouldn’t BE a function.
x-axis Symmetry
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Even, Odd or Neither?Graphically
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f x x x( ) 3Even, Odd or Neither?
Graphically
![Page 8: Warm-Up. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.](https://reader035.fdocuments.net/reader035/viewer/2022072010/56649dce5503460f94ac29b2/html5/thumbnails/8.jpg)
Even, Odd or Neither?Graphically
![Page 9: Warm-Up. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.](https://reader035.fdocuments.net/reader035/viewer/2022072010/56649dce5503460f94ac29b2/html5/thumbnails/9.jpg)
Even, Odd or Neither?Graphically
![Page 10: Warm-Up. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.](https://reader035.fdocuments.net/reader035/viewer/2022072010/56649dce5503460f94ac29b2/html5/thumbnails/10.jpg)
Given
A function is even if for every number x in the domain.
If you plug a –x into the function and you get the original function back again, the function is even.
Same!Even Function
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Given
A function is odd if for every number x in the domain.
If you plug a –x into the function and you get the negative of the function back (all terms change signs), the function
is odd.
Odd Function
ALL signs of the terms changed!
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A function is even if for every number x in the domain.
If you plug a –x into the function and you get the original function back again, the function is even.
125 24 xxxf Is this function even?
1251)(2)(5 2424 xxxxxfYES
xxxf 32 Is this function even?
xxxxxf 33 2)()(2NO
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A function is odd if for every number x in the domain.
If you plug a –x into the function and you get the negative of the function back (all terms change signs), the function
is odd.
125 24 xxxf Is this function odd?
1251)(2)(5 2424 xxxxxfNO
xxxf 32 Is this function odd?
xxxxxf 33 2)()(2YES
![Page 14: Warm-Up. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.](https://reader035.fdocuments.net/reader035/viewer/2022072010/56649dce5503460f94ac29b2/html5/thumbnails/14.jpg)
Odd, Even, or Neither?
Even Function
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Odd, Even, or Neither?
Neither Odd or Even
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Odd, Even, or Neither?
Odd Function