11X1 T03 03 symmetry [2011]
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Transcript of 11X1 T03 03 symmetry [2011]
![Page 1: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/1.jpg)
Symmetry
![Page 2: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/2.jpg)
SymmetryOdd Functions
f x f x
![Page 3: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/3.jpg)
SymmetryOdd Functions
f x f x
The curve has point symmetry about the origin
180 If you spin it it looks the same
![Page 4: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/4.jpg)
SymmetryOdd Functions
f x f x
The curve has point symmetry about the origin
180 If you spin it it looks the same
3e.g. ,y x 1 ,yx
7 5 ,y x x 9 73 2y x x
![Page 5: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/5.jpg)
SymmetryOdd Functions
f x f x
The curve has point symmetry about the origin
180 If you spin it it looks the same
3e.g. ,y x 1 ,yx
7 5 ,y x x 9 73 2y x x
Note: “all the powers are odd”
![Page 6: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/6.jpg)
SymmetryOdd Functions
f x f x
The curve has point symmetry about the origin
180 If you spin it it looks the same
3e.g. ,y x 1 ,yx
7 5 ,y x x 9 73 2y x x
Note: “all the powers are odd”3 7e.g. Prove that is an odd functiony x x
![Page 7: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/7.jpg)
SymmetryOdd Functions
f x f x
The curve has point symmetry about the origin
180 If you spin it it looks the same
3e.g. ,y x 1 ,yx
7 5 ,y x x 9 73 2y x x
Note: “all the powers are odd”3 7e.g. Prove that is an odd functiony x x
3 7f x x x
![Page 8: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/8.jpg)
SymmetryOdd Functions
f x f x
The curve has point symmetry about the origin
180 If you spin it it looks the same
3e.g. ,y x 1 ,yx
7 5 ,y x x 9 73 2y x x
Note: “all the powers are odd”3 7e.g. Prove that is an odd functiony x x
3 7f x x x 3 7f x x x
![Page 9: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/9.jpg)
SymmetryOdd Functions
f x f x
The curve has point symmetry about the origin
180 If you spin it it looks the same
3e.g. ,y x 1 ,yx
7 5 ,y x x 9 73 2y x x
Note: “all the powers are odd”3 7e.g. Prove that is an odd functiony x x
3 7f x x x 3 7f x x x 3 7x x
![Page 10: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/10.jpg)
SymmetryOdd Functions
f x f x
The curve has point symmetry about the origin
180 If you spin it it looks the same
3e.g. ,y x 1 ,yx
7 5 ,y x x 9 73 2y x x
Note: “all the powers are odd”3 7e.g. Prove that is an odd functiony x x
3 7f x x x 3 7f x x x 3 7x x 3 7x x
![Page 11: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/11.jpg)
SymmetryOdd Functions
f x f x
The curve has point symmetry about the origin
180 If you spin it it looks the same
3e.g. ,y x 1 ,yx
7 5 ,y x x 9 73 2y x x
Note: “all the powers are odd”3 7e.g. Prove that is an odd functiony x x
3 7f x x x 3 7f x x x 3 7x x 3 7x x f x
![Page 12: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/12.jpg)
SymmetryOdd Functions
f x f x
The curve has point symmetry about the origin
180 If you spin it it looks the same
3e.g. ,y x 1 ,yx
7 5 ,y x x 9 73 2y x x
Note: “all the powers are odd”3 7e.g. Prove that is an odd functiony x x
3 7f x x x 3 7f x x x 3 7x x 3 7x x f x odd function
![Page 13: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/13.jpg)
Even Functions
f x f x
![Page 14: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/14.jpg)
Even Functions
f x f x
The curve has line symmetry about the y axis the y axis is an axis of symmetry
![Page 15: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/15.jpg)
Even Functions
f x f x
The curve has line symmetry about the y axis the y axis is an axis of symmetry
2e.g. ,y x 2 4,y x 6 4 23 2 27y x x x
![Page 16: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/16.jpg)
Even Functions
f x f x
The curve has line symmetry about the y axis the y axis is an axis of symmetry
2e.g. ,y x 2 4,y x 6 4 23 2 27y x x x
Note: “all the powers are even”
![Page 17: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/17.jpg)
Even Functions
f x f x
The curve has line symmetry about the y axis the y axis is an axis of symmetry
2e.g. ,y x 2 4,y x 6 4 23 2 27y x x x
Note: “all the powers are even”2e.g. Prove that 4 is an even functiony x
![Page 18: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/18.jpg)
Even Functions
f x f x
The curve has line symmetry about the y axis the y axis is an axis of symmetry
2e.g. ,y x 2 4,y x 6 4 23 2 27y x x x
Note: “all the powers are even”2e.g. Prove that 4 is an even functiony x
2 4f x x
![Page 19: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/19.jpg)
Even Functions
f x f x
The curve has line symmetry about the y axis the y axis is an axis of symmetry
2e.g. ,y x 2 4,y x 6 4 23 2 27y x x x
Note: “all the powers are even”2e.g. Prove that 4 is an even functiony x
2 4f x x 2 4f x x
![Page 20: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/20.jpg)
Even Functions
f x f x
The curve has line symmetry about the y axis the y axis is an axis of symmetry
2e.g. ,y x 2 4,y x 6 4 23 2 27y x x x
Note: “all the powers are even”2e.g. Prove that 4 is an even functiony x
2 4f x x 2 4f x x 2 4x
![Page 21: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/21.jpg)
Even Functions
f x f x
The curve has line symmetry about the y axis the y axis is an axis of symmetry
2e.g. ,y x 2 4,y x 6 4 23 2 27y x x x
Note: “all the powers are even”2e.g. Prove that 4 is an even functiony x
2 4f x x 2 4f x x 2 4x
f x
![Page 22: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/22.jpg)
Even Functions
f x f x
The curve has line symmetry about the y axis the y axis is an axis of symmetry
2e.g. ,y x 2 4,y x 6 4 23 2 27y x x x
Note: “all the powers are even”2e.g. Prove that 4 is an even functiony x
2 4f x x 2 4f x x 2 4x
f x even function
![Page 23: 11X1 T03 03 symmetry [2011]](https://reader033.fdocuments.us/reader033/viewer/2022052602/559cd2df1a28ab607f8b477a/html5/thumbnails/23.jpg)
Even Functions
f x f x
The curve has line symmetry about the y axis the y axis is an axis of symmetry
2e.g. ,y x 2 4,y x 6 4 23 2 27y x x x
Note: “all the powers are even”2e.g. Prove that 4 is an even functiony x
2 4f x x 2 4f x x 2 4x
f x even function
Exercise 3C; 1aceg, 2, 4aceg, 5, 6bdfh, 8adf, 9, 10*