Question 1140124
Table A- 
{{{x}}}|{{{y=3^x}}}
{{{-1}}}|{{{1/3}}}...{{{y=3^-1=1/3}}}
{{{0}}}|{{{1}}}........{{{y=3^0=1}}}
{{{1}}}|{{{3}}}.......{{{y=3^1=3}}}
{{{2 }}}|{{{9}}}........{{{y=3^2=9}}}

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(-1,1/3,.12),circle(0,1,.12),
locate(-1,1/3,p(-1,1/3)),locate(0,3,p(0,3)),

circle(1,3,.12),circle(2,9,.12),
locate(1,3,p(1,3)),locate(2,9,p(2,9)),

 graph( 600, 600, -10, 10, -10, 10,3^x)) }}}




Table B-

first find  the inverse:

{{{y=3^x}}}........swap {{{x}}} and {{{y}}}

{{{x=3^y}}}..........solve for {{{y}}}, take a log of both sides

{{{log(x)=log(3^y)}}}

{{{log(x)=ylog(3)}}}

{{{y=log(x)/log(3)}}}

{{{x}}}|{{{y}}}
{{{-1}}}|{{{y}}}.............{{{y=log(-1)/log(3)}}}->no real solution
{{{0}}}|{{{y}}}.............{{{y=log(0)/log(3)=-infinity}}}->-∞
{{{1}}}|{{{0}}}.............{{{y=log(1)/log(3)=0}}}
{{{2}}}|{{{0.63}}}.............{{{y=log(2)/log(3)=0.63}}}

b. Plot the points from TABLE B t sketch a graph of the inverse 

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(1,0,.12),circle(2,0.63,.12),locate(1,-0.5,p(1,0)),locate(2,0.63,p(2,0.63)),
 graph( 600, 600, -10, 10, -10, 10,log(10,x)/log(10,3))) }}}



c. Use your graph from (b) to give the natural domain and range of the inverse

domain :{ {{{x}}} element {{{R}}} : {{{x>0}}} } (all positive real numbers)
and 
range: {{{R }}}(all real numbers)