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(Section 1.7: Symmetry Revisited)
1.7.1
SECTION 1.7: SYMMETRY REVISITED
LEARNING OBJECTIVES
• Recognize short cuts for identifying even functions and odd functions.
• Be able to justify those short cuts using proofs.
• Use equations to identify symmetries in their graphs.
PART A: DISCUSSION
• In Section 1.3, we defined even functions
and odd functions
, whose graphs in the
xy
plane were
symmetric
about the
y
axis
and the
origin
, respectively.
• We will now
systematize
our study of these functions and their graphical
symmetries. We will discuss useful
short cuts
for identifying even functions and
odd functions, and we will show how to
prove
them rigorously. We will also
extend related symmetries to graphs of
general equations
in
x
and
y
.
• A zero function
f
, where
fx
()
=
0 (on any domain), will be called a trivial function
.
If its domain is symmetric about 0, then it is
both
even and odd.
• Symmetry will prove helpful when graphing functions and equations
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 Spring '09
 Equations

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