Question 598044
f(x)= -2(3)^x +1
:
{{{-2(3^x)+1}}} = 0
{{{-2(3^x)}}} = -1
divide both sides by -2
{{{3^x}}} = {{{(-1)/(-2)}}}
:
{{{3^x}}} = .5
using nat logs
x*ln(3) = ln(.5)
x = {{{ln(.5)/ln(3)}}}
x = -.631
:
To graph this make a table of values starting with x=-2, the every half unit to x=+2
Using a calc: 
y = -2(3^-2) + 1 
y = -2(.111) + 1
y = .777
Find y for each value of x, 
 x | y
-------
-2.0|.78
-1.5|.62
-1.0|.33
-0.5|-.15
0.0 |-1.0
+0.5|-2.5
+1.0|-5
+1.5|-9.4
+2.0|-17
Your graph should look alot like this
{{{graph( 300, 200, -2, 5, -20, 4, -2(3^x)+1) }}}