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Symmetry
SymmetryOdd Functions
f x f x
SymmetryOdd Functions
f x f x
The curve has point symmetry about the origin
180 If you spin it it looks the same
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
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”
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
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
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
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
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
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
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
Even Functions
f x f x
Even Functions
f x f x
The curve has line symmetry about the y axis the y axis is an axis of symmetry
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
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”
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
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
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
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
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 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
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*
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