Question 1198009
1. Complete the table below (use fractions - not decimals!) and use it to graph the function

 {{{f(x) = 3^x}}}

{{{x}}}|{{{y}}}   
{{{-2}}}|{{{1/9}}}   .....{{{f(-2) = 3^(-2)=1/3^2=1/9}}}
{{{-1}}}|{{{1/3}}}    .....{{{f(-1) = 3^(-1)=1/3^1=1/3}}}
{{{0}}}|{{{1}}}    .....{{{f(0) = 3^0=1}}}
{{{1}}}|{{{3}}}    .....{{{f(1) = 3^1=3}}}
{{{2}}}|{{{9}}}    .....{{{f(2) = 3^2=9}}}


Domain ___{{{R}}} (all real numbers)


Range _____{ {{{f(x) }}} element {{{R}}} :{{{f(x)>0}}} } (all positive real numbers)

coordinates of the y-intercept __{{{f(x) =3}}}


equation of the asymptote ____Horizontal asymptote    {{{f(x) =0}}}

means {{{3^x->0}}} as {{{x->-infinity}}}





2. Using your knowledge of inverses, prepare a table of values for the inverse of the function in
problem #1.
Graph the inverse on the same coordinate system as the function.
Label each graph appropriately as {{{f(x)}}} or {{{f^-1(x)}}}.

Answer the following for the inverse function:

The equation of the inverse is {{{f^-1(x)}}} = ______________

recall that  {{{f(x) = y}}}, so

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

{{{x= 3^y}}}................solve for {{{y}}}

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

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

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

your inverse is {{{f^-1(x)=log(x)/log(3)}}}

 to make a table of values for the inverse of the function just switch  the values of variables

{{{x}}} |{{{y}}}  
{{{1/9}}}|{{{-2}}}
{{{1/3}}}|{{{-1}}}
{{{1}}}|{{{0}}}
{{{3}}}|{{{1}}}
{{{9}}}|{{{2}}}

Domain ____

will be what was a range of original function; { {{{x}}} element {{{R}}} :{{{x>0}}} }

Range _______a domain of original function;{{{R}}} (all real numbers)

coordinates of the x-intercept _______{{{x=1}}}
equation of the asymptote _____Vertical: {{{x=0}}}