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2.1 Symmetry

2.1 Symmetry. When a figure has line symmetry, it can be folded on its line of symmetry and the two have to coincide exactly There are 3 symmetries important in graphing. (–a, b). (a, b). (a, b). (a, b). (a, –b). (–a, –b). Typically can do two types of problems

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2.1 Symmetry

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  1. 2.1 Symmetry

  2. When a figure has line symmetry, it can be folded on its line of symmetry and the two have to coincide exactly There are 3 symmetries important in graphing (–a, b) (a, b) (a, b) (a, b) (a, –b) (–a, –b)

  3. Typically can do two types of problems Ex 1) Given the point , determine coordinates of the point that satisfies specified symmetry. origin c) x-axis b) y-axis (a, b)  (–a, b) (a, b)  (–a, –b) (a, b)  (a, –b)

  4. Ex 2) Determine symmetry. Graph using the properties of symmetry. x-axis –y = x2 – 4 y = –x2 + 4 not equivalent y-axis y = (–x)2 – 4 y = x2 – 4 equivalent origin –y = (–x)2 – 4 –y = x2 – 4 not equivalent Choose only positive x’s & negative x’s will match

  5. Ex 3) Use graphing calculator to find symmetry. x = 2

  6. We can also have graphs symmetric to line y = x Test: switch x & y and get equivalent eqtn (x, y)  (y, x) Even Function If f (–x) = f (x) symmetric to y-axis Odd Function If f (–x) = – f (x) symmetric to origin

  7. Ex 4) Determine if function is even, odd or neither a) odd b) neither c) even

  8. Homework #201 Pg 61 #1–31 odd, 39, 41–46 all

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