Question

Let f(x)=4√x
If g(x) is the graph of f(x) shifted up 3 units and right 2 units, write a formula for g(x).
g(x)=

Answer 1

to shift up 3 we simply add 3,
so far:
y = 4√x + 3

to move to the right 2, we replace the x with (x-2)

final :
<b>g(x) = 4√(x-2) + 3</b>

check: on Wolfram
https://www.wolframalpha.com/input/?i=graph+y+%3D+4%E2%88%9Ax+%2C+y+%3D+4%E2%88%9A%28x-2%29+%2B+3

( look only at the curves in quadrant I, ignore the "imaginary" parts of the graph )

Answer 2

moving up
if x = 0, g = 3
g(x) = 3 + f(x)
moving sideways
g( x) = f(x-2)
so
g(x) = 3 + f(x-2)
g(x) = 3 + 4 sqrt ( x-2)