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2.1 Symmetry.

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Presentation on theme: "2.1 Symmetry."— Presentation transcript:

1 2.1 Symmetry

2 There are 3 symmetries important in graphing
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 With Respect To x-axis y-axis origin Definition If (a, b) is on graph, so is (a, –b) so is (–a, b) so is (–a, –b) Illustration Test Substituting –y for y results in equivalent equation Substituting –x for x results in equivalent equation Substituting –x for x AND –y for y results in equivalent equation (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 b) y-axis c) x-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 x y 1 2 –4 –3 x y –1 –2 –3 Choose only positive x’s & negative x’s will match

5 Ex 3) Use graphing calculator to find symmetry.

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 # Pg #1–31 odd, 39, 41–46 all


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