Answer:
[tex]g(x)=3\cdot3^x-2[/tex]
Step-by-step explanation:
The base function is [tex]f(x)=3^x[/tex] .
The transformed graph now has a horizontal asymptote of y=-2.
So the transformed equation is of the form [tex]g(x)=a(3^x)-2[/tex]
We now have to determine the value of [tex]a[/tex]
[tex]g(0)=1[/tex]
[tex]-1=a*3^{-1}-2[/tex]
[tex]1=a*3^{-1}[/tex]
[tex]a=3[/tex]
Therefore the equation is [tex]g(x)=3\cdot3^x-2[/tex]
