Answer:
[tex]g(x)=4\cdot 2^x[/tex]
Step-by-step explanation:
From the graph,
[tex](0,1)\rightarrow (-2,1)\\ \\(1,2)\rightarrow (-1,2)\\ \\(2,4)\rightarrow (0,4)[/tex]
It can be rewritten as
[tex](0,1)\rightarrow (0+(-2),1+0)\\ \\(1,2)\rightarrow (1+(-2),2+0)\\ \\(2,4)\rightarrow (2+(-2),4+0)[/tex]
This is translation of the function f(x) 2 units to the left and 0 units up or down. This translation will give the function
[tex]g(x)=2^{x+2}[/tex]
that is the same as
[tex]g(x)=2^x\cdot 2^2\\ \\g(x)=4\cdot 2^x[/tex]
