Answer:
[tex]g(x) = 3^{x-2} -1[/tex]
Step-by-step explanation:
The parent graph is f(x) = 3^x
When we compare the parent graph f(x) = 3^x with given graph
We can see that the given graph is shifted 2 units to the right and 1 unit down
When we shift 2 units to the right then we put x-2 in the exponent
Then when we shift 1 unit down, put -1 at the end
So function g(x) becomes [tex]g(x) = 3^{x-2} -1[/tex]
LEt check with given point (2,0) and (3,2)
[tex]g(x) = 3^{x-2} -1[/tex]
(2,0)
[tex]0 = 3^{2-2} -1[/tex]
[tex] 0=0[/tex] True
(3,2)
[tex]2 = 3^{3-2} -1[/tex]
[tex]2=2[/tex] True
