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MAT 017C AOZ in ,
10.1 Functions of two or more variables
Domain and range
polynomials : ex. x2+3xyt4y2no restriction
Domain : 1132
logarithms : ln x,xelo , a)
ln ( y- xz )
,
{ ( x. up EIRYY - x2 > 03
lntsxy -4yd ,{ ( xy )eR43xy -44>0 }national functions cxtstfxz) { xeklx -3-+9×-2*03
4xy÷3xr{ ( x. g)EIRY4xy -3×2-+03Ft { 1 x.g)EIRY 1 xiy ) * ( 0,0)}
square roots n2¥2{ XEIR 1×2-2>-03
xFyt4xy { lxyletltlxzyttlxyzo}
square roots Kfz { XEIRIX ' -2>-03
FELIX { lxyletltlxzyttlxyzo}1- x4y2 > 0
lnx 'ty' lnlxztyyto
{ lxy)HR2|x4y2tl,
xityzto }#
(pen tx 'D
C- a a) xtx ,x)
Range : polynomial"
Range"
* " * .
#w#hI¥Yhy. #tby
' er
lnlx ) # tax )=lR
KT ( o ,x )tx fx ,o1U( 0,4=112403
{xektx.to#yx2ty2tlx2ty2-tO
to ,0)U( ax )&n[lnhityy ]=tao)U( op )
I
tank]=tx0)u(and
x > 0
Dom
ln(#x2) Dom :{ ( xiy )EM1y-x2 > 03
#¢Ran:C. andY
> *
Runs Y> x2}={ ZEIRIZ > 0 )
THEY.
Dom : 1132
ffx ,y)=xTtyRan :{ ZEIRIZZO)zaxtty( o ,x ){axtyc=
0,1/2,3E Rants )
t.a.FI?Fx.+y.=i• z=xftyn x2tyh=4
\_|¥→=#tfx4y±q
"
¥←it#¥n~#?±¥f-j
y = X
y=x2hyena
., III §�1� positive x- axis → y=o
�2� positive y- axis →
xto
oleaxIIYo0IfiaxE-xkat@lgee02oIyIlgetFtget-zfEio.o
,
'IF¥⇒NEy¥
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