2.7 Analyzing Graphs of Piecewise Functions

ANALYZIng GRAPHS Of
functions A
-




preceive functions
Analyzing Symmetry
property that makes one part of the like of another
graph look a
copy part ...

X-axis symmetry y-axis symmetry origin symmetry
-




:
-




- - -




Lis
-
> >

~ T




part below X-axis is of the left & right unchanged
a
parts graph is when
reflected version of the of copies of
reflected first across X-axis,
y-axis are

point above X-axis each other then across y-axis



tests for symmetry

I I
X-axis symmetry y-axis symmetry origin symmetry
formula
X X3 X

Y
-




Y
-

X
-




formula stays the same stays the

Y
formula
stays...
the same when when
... --Y same when
..

with respect to
...
Decide if the following expressions symmetric
examples
are


a) the X-axis a)yz x3 3 = -



b)(y) =
x2 - 2

b) the y-axis ·
testing X-axis symmetry
·
testing X-axis
symmetry
c) the origin or neither
y + y ( y)
-




= >
=




yz
=
x3 3
x3 3
-




-
same
given
as
formula
/Same armula

symmetric with respect to
y-axis !
symmetric with respect to
y-axis ! ·
testing y-axis symmetry
·
testing y-axis symmetry

I
not the X-
X/IYEEXLSamT
-




X + -




xyz =
( x)3 3 same given
-
-




> x3 3 formula
y with to X-axis !
symmetric respect
= =
-
-




with respect to X-axis !
NOT symmetric ·
testing origin symmetry
·
testing origin symmetry (x)3 2 same as
x/EyS = /1-yl =
=

*- not T -




given
-




same given ly) X3 2 ra !
y - y
= = -
-




formula
NOT symmetric about the origin ! symmetric about the origin !