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¥