Question 117748
I'll do the first one to show you how to do these


{{{f(x)=-2*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)=-2*3^0}}}  Plug in {{{x=0}}}


{{{f(0)=-2*1}}}  Raise 3  to the zeroth power to get 1


{{{f(0)=-2}}}  Multiply -2 by 1 to get -2


So when {{{x=0}}}, {{{y=-2}}}. So our  first point is (0,-2)



----Now lets find another point----
{{{f(1)=-2*3^1}}}  Plug in {{{x=1}}}


{{{f(1)=-2*3}}}  Raise 3  to the first power to get 3


{{{f(1)=-6}}}  Multiply -2 by 3 to get 6


So when {{{x=1}}}, {{{y=-6}}}. So our  second point is (1,-6)



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


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


{{{f(2)=-18}}}  Multiply -2 by 9 to get -18


So when {{{x=2}}}, {{{y=-18}}}. So our  third point is (2,-18)



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


{{{f(3)=-2*27}}}  Raise 3  to the third power to get 27


{{{f(3)=-54}}}  Multiply -2 by 27 to get -54


So when {{{x=3}}}, {{{y=-54}}}. So our  fourth point is (3,-54)




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


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>-2</TD></TR> 
<TR><TD> 1</TD><TD>-6</TD></TR> 
<TR><TD> 2</TD><TD>-18</TD></TR> 
<TR><TD> 3</TD><TD>-54</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing( 900, 900, -10, 10, -10, 10,
  grid( 1 ),circle(0,-2,0.05),
circle(0,-2,0.08),
circle(1,-6,0.05),
circle(1,-6,0.08),
circle(2,-18,0.05),
circle(2,-18,0.08),
circle(3,-54,0.05),
circle(3,-54,0.08))}}}



Connect the points to form the graph {{{y=-2*3^x}}}

{{{drawing( 900, 900, -10, 10, -10, 10,
grid( 1 ),
graph( 900, 900, -10, 10, -10, 10, -2*3^x),
circle(0,-2,0.05),
circle(0,-2,0.08),
circle(1,-6,0.05),
circle(1,-6,0.08),
circle(2,-18,0.05),
circle(2,-18,0.08),
circle(3,-54,0.05),
circle(3,-54,0.08))}}} Graph of {{{y=-2*3^x}}} through the points solved for earlier