Question

Could someone explain/answer this?

Answer 1

f(x) + n - shift a graph n units up

f(x) - n - shift a graph n units down

f(x + n) - shift a graph n units left

f(x - n) - shift a graph n units right

We have $f(x)=\sqrt{x}$

shift a graph 4 units left → $f(x+4)=\sqrt{x+4}$

next, shift a graph 6 units up → $f(x+4)+6=\sqrt{x+4}+6$

Answer: $D)\ g(x)=\sqrt{x+4}+6$

Answer 2

in general, the graph of y = f(x-a) is a shift a units right if a is positive and shift of a units left if a is negative. for example, y = f(x-2) is 2 units right of f(x) and y=f(x+2) is 2 units LEFT.

in general, the graph of y = f(x) + a is a shift a units up if a is postiive and a units down if a is negtaive. For example, y = f(x) + 4 is 4 units up and y=f(x)-4 is a shift of 4 units down.

Note that f(x) = sqrt(x) here, so we have f(x+4) = sqrt(x+4) for 4 units left. Then you do f(x+4) + 6 = sqrt(x+4) + 6 for 6 units up.

Your answer is g(x) = sqrt(x+4) + 6