Answer:[tex]g(x)=8(2^x)[/tex]Step-by-step explanation:Here we are given with parent function [tex]f(x)=2^x[/tex] and the graph which shows that the function g(x).We are asked to guess the function g(x).We are given the two coordinates on g(x)(0,8) and (2,32)Hence for x = 0 , g(x)= 8And for x=2, g(x)= 32 Let us say that the translated function is represented by[tex]g(x)=a2^x+b[/tex][tex]g(0)=a\times 2^0+b[/tex]Hence[tex]a \times 2^0+b=8[/tex][tex]a +b=8[/tex] --------------- (i)also[tex]g(2)=32[/tex]Hence[tex]a\times 2^2+b=32[/tex][tex]4a+b=32[/tex] -------------------(ii)Subtracting (i) from (ii) we get[tex]3a=34[/tex]Hence a = 8Now putting this value of a in (i)[tex]8+b=8[/tex]B=0Hence [tex]g(x)=8 \times 2^x +0[/tex][tex]g(x)=8(2^x)[/tex]