Given:
The function f(x) represents the blue curve.
The function g(x) represents the red curve.
Checking the x-values, we can see that the x-values of g(x) is double of the x-values of f(x).
Therefore, the transformation that occurs between both of them is
[tex]g(x)=f(0.5x)[/tex]Checking for confirmation
[tex]\begin{gathered} when\text{ x=0} \\ f(x)=f(0)=1 \\ g(x)=f(0.5x)=f(0.5\times0)=f(0)=1 \end{gathered}[/tex]Hence, from the result above we can conclude that our transformation rule is correct.
Therefore, the answer is
[tex]g(x)=f(0.5x)[/tex]