Math 1330
Section 1.2
Tests for Symmetry:
A function has symmetry in the
x
axis if
(
x
,

y
29
is on the graph of
f
whenever
(
x
,
y
29
is.
Test: leave
x
alone and substitute
–y
for
y
. If you get an equivalent equation, your function has
symmetry in the
x
axis.
A function has symmetry in the
y
axis if
(
x
,
y
29
is on the graph of
f
whenever
(
x
,
y
29
is.
Test: leave
y
alone and substitute
–x
for
x
. If you get an equivalent equation, your function has
symmetry in the
y
axis.
A function has symmetry in the origin if
(
x
,

y
29
is on the graph of
f
whenever
(
x
,
y
29
is.
Test: substitute
–x
for
x
and
–y
for
y
. If you get an equivalent equation, your function has symmetry
in origin.
Note: an equation can have more than one type of symmetry
Example 4:
Test the equation for symmetry:
g1876
g2870
+g1877
g2870
=15
Even and Odd Functions
A function
f
is even if
f
(

x
)
=
f
(
x
) for all x in the domain of
f
. Since an even function is symmetric
with respect to the yaxis, the points (

x
,
y
) and (
x
,
y
) are on the same graph.
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Math 1330
Section 1.2
A function is odd if
f
(

x
)
=
f
(
x
) for all
x
in the domain of the function. Odd functions have
symmetry with respect to the origin. Here is an example of an odd function
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 Spring '10
 N/A
 Even and odd functions

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