Step-by-step explanation:
shifts up and down are easy. we only need to adjust the original functional value by the constant of the shift.
the whole curve of the function stays optically the same, but as every calculated functional value is increased or decreased by the same value, the whole curve simply shifts up or down.
shift down 3 units means "f(x) - 3".
so, just for the shift down we would have
g(x) = 2×sqrt(x) - 3
but we also need to shift right by 5 units.
what does that mean ?
it means that we want to have every functional value as before, but ... 5 units of x "later" (to the right) than before.
so, e.g.
f(0) = 2×sqrt(0) = 2×0 = 0
so, we still want that 0 as functional value, but it should happen now at x = 5 instead of x = 0.
in other words
g(5) = f(0)
and further on
g(6) = f(1)
g(7) = f(2)
...
but also
g(4) = f(-1)
...
g(0) = f(-5)
and so on.
now look at the structure :
this means
g(x) = f(x-5)
and so,
g(x) = 2×sqrt(x-5) - 3
this function is now exactly like f(x), just shifted 5 units right and 3 units down.
