Let f ( x ) = 4 √ x If g ( x ) is the graph of f ( x ) shifted up 2 units and left 5 units, write a formula for g ( x )

Question

Let If  is the graph of  shifted up 2 units and left 5 units, write a formula for 

Answer 1

g(x) = 4√(x+5) + 2

Hey, if you have f(x) = x:

to shift left by h units, replace x with x+h and to shift up by k units, replace f(x) by f(x)-k.

So: f(x) = 4√x

f(x) = 4√(x+5) [shifted left by 5 units]

f(x) - 2 = 4√(x+5) [shifted up by 2 units]∴

∴ g(x) = 4√(x+5) + 2

Answer 2

If you were to shift the graph up 2 and left 5, then the formula of the graph would be y=√(x+5)+2.