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2.1 Symmetry

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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

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)

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

Ex 3) Use graphing calculator to find symmetry.

x = 2

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

Ex 4) Determine if function is even, odd or neither

a)

odd

b)

neither

c)

even

#201 Pg 61 #1–31 odd, 39, 41–46 all