Let's take it step by step.Translation of 2 units down: This means that we take the graph of f(x)=x and move it down 2 units. This can be done by subtracting 2 from each y-coordinate.
Horizontal shrink by a factor of 2/3: This means that we take the graph of f(x)=x and shrink it horizontally by a factor of 2/3. This can be done by multiplying each x-coordinate by 2/3.
So, the function g(x) that represents the translation of 2 units down and a horizontal shrink by a factor of 2/3 of the graph of f(x)=x is:
g(x) = (x-2) * (2/3)
This simplifies to:
g(x) = (2x/3) - 4/3