Question

In the graph below the blue curve is the graph of y=f(x) and the red curve is the graph of y=g(x)

Answer 1

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

`g(x)=f(0.5x)`

Checking for confirmation

`\begin{gathered} when\text{ x=0} \\ f(x)=f(0)=1 \\ g(x)=f(0.5x)=f(0.5*0)=f(0)=1 \end{gathered}`

Hence, from the result above we can conclude that our transformation rule is correct.

Therefore, the answer is

`g(x)=f(0.5x)`