Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
Notes #18: Symmetry and Coordinate Graphs
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
Even Functions
Even Functions have symmetry with respect to the y­axis.
f(­x) = f(x)
In other words...
Plug in ­x for x. If it recreates the original function, then it is an even function with y­axis symmetry.
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
f(x) = x2
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
Odd Functions
Odd Functions have symmetry with respect to the origin.
f(­x) = ­f(x)
In other words...
Plug in ­x for x and ­y for y. If it recreates the original function, then it is an odd function and has origin symmetry.
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
f(x) = x
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
X­axis Symmetry
A graph is symmetric to the x­axis if (a, ­b) ∈ S if and only if (a, b) ∈ S in other words...
­f(x) = f(x)
in other, other words...
Plug in ­y for y. If it recreates the original function, then it has x­axis symmetry.
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
Symmetry with Respect to a line
If an equation is symmetric with respect to y=x, then (b, a) ∈ S if and only if (a, b) ∈ S
In other words...
Plug in y for x and x for y. If you can
recreate the original equation, then it is
symmetric with respect to y=x.
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
Symmetry with Respect to a line
If an equation is symmetric with respect to y=­x, then (b, a) ∈ S if and only if (-a, -b) ∈ S
In other words...
Plug in -x for y and -y for x. If you can
recreate the original equation, then it is
symmetric with respect to y=-x.
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
Do Now: Determine if the following are symmetric with respect to the y­axis, x­axis, line y = x, or line y = ­x.
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
Symmetric to y­axis
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
Symmetric to x­axis
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
Symmetric to origin
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
Determine if the following graph is symmetric with respect to the y­axis, x­axis, both, or neither. Use this information to graph the relation.
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
Determine if the following graph is symmetric with respect to the y­axis, x­axis, both, or neither. Use this information to graph the relation.
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Notes #18 Symmetry and Coordinate Graphs
October 24, 2012
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