Question 110363
{{{f(x)=3^x}}} Start with the given expression

In order to plot an exponential function, we need to plot some points

We can start at any x value, so lets start at x=0


{{{f(0)=3^0}}}  Plug in {{{x=0}}}


{{{f(0)=1}}}  Raise 3  to the zeroth power to get 1


So when {{{x=0}}}, {{{y=1}}}. So our  first point is (0,1)



----Now lets find another point----
{{{f(1)=3^1}}}  Plug in {{{x=1}}}


{{{f(1)=3}}}  Raise 3  to the first power to get 3


So when {{{x=1}}}, {{{y=3}}}. So our  second point is (1,3)



----Now lets find another point----
{{{f(2)=3^2}}}  Plug in {{{x=2}}}


{{{f(2)=9}}}  Raise 3  to the second power to get 9


So when {{{x=2}}}, {{{y=9}}}. So our  third point is (2,9)




===============================================================================


Now lets make a table of the values we have calculated

<pre>
<TABLE width=500>

<TR><TD> x</TD><TD>y</TD></TR>

<TR><TD> 0</TD><TD>1</TD></TR> 
<TR><TD> 1</TD><TD>3</TD></TR> 
<TR><TD> 2</TD><TD>9</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing( 900, 900, -10, 10, -10, 10,
  grid( 1 ),circle(0,1,0.05),
circle(0,1,0.08),
circle(1,3,0.05),
circle(1,3,0.08),
circle(2,9,0.05),
circle(2,9,0.08))}}}



Connect the points to form the graph {{{y=3^x}}}

{{{drawing( 900, 900, -10, 10, -10, 10,
grid( 1 ),
graph( 900, 900, -10, 10, -10, 10, 3^x),
circle(0,1,0.05),
circle(0,1,0.08),
circle(1,3,0.05),
circle(1,3,0.08),
circle(2,9,0.05),
circle(2,9,0.08))}}} Graph of {{{y=3^x}}} through the points solved for earlier