#f(x) = (1/3)^x - 3#
Before we start plotting points, let's first get an idea of some of the characterics of #f(x)#
#lim_(x->+oo) f(x) = 0 -3 = -3#
We should note that #f(x) -> -3# very rapidly.
I.e. We wont need very many points #x>0#
#lim_(x->-oo) f(x) = lim_(x->+oo) 3^x-3 = +oo#
Again #f(-x) -> oo# quite rapidly.
#f(0) = (1/3)^0 -3 = 1-3 =-2#
So, #(0, -2)# is a point on our graph
#f(x) =0 -> (1/3)^x = 3#
#3^(-x) = 3^1 -> x=-1#
So, #(-1, 0)# is another point on our graph.
Calculating other points:
#f(1) = 1/3-3 approx -2.667#
#f(2) = 1/9-3 approx -2.889#
#f(3) = 1/27-3 approx -2.963#
#f(-2) = 9-3 =6#
#f(-3) = 27-3 =24#
We can use the chracteristics and calculated points of #f(x)# to plot a graph as produced below.
graph{(1/3)^x-3 [-7.9, 7.9, -3.935, 3.97]}
