The graph of f in blue is translated a whole number of units

The graph of f (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of g (in red). The function f is defined by f(x) = Squareroot x. Write down the expression for g(x).

Solution

f(x) = x

In graph of g(x) , it shifts downward by 2 and right by 4

Shifts right - i.e y will be zero at x=4 , so (x-4)

and shifts downward by 2 then , y = -2 + (x-4)

So, g(x) = -2 + (x-4)