Answer:
[tex]g(x) = {3}^{x - 2} - 7[/tex]
Step-by-step explanation:
As we can see, the graph of transformation of f(x) is translated to the right and down.
then, g(x) = f(x - a) - b, where a & b > 0.
from the options, there are 4 translated function of f(x).
but on the second option
[tex] {3}^{x + 7} - 2 = {3}^{x - ( - 7)} - 2[/tex]
a < 0, then it's not the answer we need, same as third option that makes only first and fourth left.
from the picture, horizontal asymptote of f(x) is y = 0.
on g(x) horizontal asymptote is y = -b, where -10 < -b < -5.
and from the options that are left, we can see only fourth option that satisfies what we need.
