Answer:
g(x) = [tex]8 (3)^{x-1} + 6[/tex]
Step-by-step explanation:
Given the function: [tex]f(x) = 8(3)^{x-2} + 2[/tex]
For the parent function f(x) and a constant k >0,
then,
the function given by
g(x) = kf(x) can be sketched by vertically stretching f(x) by a factor of k if k>1
or
if 0 < k < 1 , then it is vertically shrinking f(x) by a factor of k
.
As per the given statement that the graph of f(x) is stretched vertically by a factor of 3 i.e
k = 3 >1
so, by definition
g(x) = 3 f(x) = [tex]3 \cdot (8(3)^{x-2} + 2) = 3 \cdot 8 (3)^{x-2} +6 = 8 (3)^{x-1} + 6[/tex] [Using [tex]a^n \cdot a^m = a^{n+m}[/tex] ]
Therefore, the equation of g(x) = [tex]8 (3)^{x-1} + 6[/tex]
