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)= 8
And 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 = 8
Now putting this value of a in (i)
[tex]8+b=8[/tex]
B=0
Hence [tex]g(x)=8 \times 2^x +0[/tex]
[tex]g(x)=8(2^x)[/tex]
