Question

What is the equation of the transformed function, g(x), after the transformations are applied to the graph of

the base function f(x)=√x to obtain the graph of g(x)?
A g(x) +4=√√√x+4
B g(x)=√√x+4 +5
C g(x) +5=√√x+4
D g(x)=√√x+5+4

Answer 1

Check the picture below, that's just a transformations template

so since we know that f(x) = √x, that means when x = 0, y = 0, so it touches the origin, so f(x) is the graph down below.

now, f(x) has moved to the left by 5 units and up by 4 units, based on the template that means C = 5 and D = 4 whilst B = 1

`g(x)=\stackrel{A}{1}\sqrt{\stackrel{B}{1}x+\stackrel{C}{5}} ~~ +\stackrel{D}{4}\implies g(x)=√(x+5) ~~ +4`